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AP Board Class 7 Maths Chapter 5 Triangle and Its Properties Ex 3 Textbook Solutions PDF: Download Andhra Pradesh Board STD 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Book Answers |
Andhra Pradesh Board Class 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Textbooks Solutions PDF
Andhra Pradesh State Board STD 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Books Solutions with Answers are prepared and published by the Andhra Pradesh Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of AP Board Class 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 7th Maths Chapter 5 Triangle and Its Properties Ex 3 solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Andhra Pradesh Board STD 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Textbooks. These Andhra Pradesh State Board Class 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Andhra Pradesh Board.Andhra Pradesh State Board Class 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Books Solutions
Board | AP Board |
Materials | Textbook Solutions/Guide |
Format | DOC/PDF |
Class | 7th |
Subject | Maths |
Chapters | Maths Chapter 5 Triangle and Its Properties Ex 3 |
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AP Board Class 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Textbooks Solutions with Answer PDF Download
Find below the list of all AP Board Class 7th Maths Chapter 5 Triangle and Its Properties Ex 3 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:Question 1.
Find the value of the unknown ‘x’ in the following triangles.
Solution:
i) In ΔABC
∠A + ∠B + ∠C = 180° (angle sum property
x° + 50° + 60° = 180°
x° + 110° = 180°
x° = 180° – 110°
ii) In ΔPQR,
∠P + ∠Q + ∠R = 180° (angle – sum property)
90° + 30° + x° = 180°
120° + x° – 180°
x° = 180° – 120°
∴ x° = 60°
iii) In ΔXYZ,
∠X + ∠Y + ∠Z = 180° (angle – sum property)
30°+110° + x° =180°
140° + x° = 180°
x° = 180° – 140°
∴ x° = 40°
Question 2.
Find the values of the unknowns ‘x ‘and ‘y ‘in the following diagrams.
Solution:
i) In ΔPQR,
x° + 50° = 120° (exterior angle property)
x°= 120°- 50°
x°= 70°
Also
∠P + ∠Q +∠R = 180° (angle – sum property)
70° + 50° + y° = 180°
120° + y° = 180°
y° = 180° – 120°
y° = 60°
(OR)
y° + 120° = 1800 (linear pair of angles)
y° = 180°- 120°
∴ y° = 60°
ii) In the figure ΔRST,
x° = 80° (vertically opposite angles)
also ∠R + ∠S + ∠T = 180° (angle – sum property)
80° + 50°+ y°= 180°
130° + y° = 180°
y° = 180° – 130°
∴ y° = 50°
iii) m ΔMAN,
x° = ∠M + ∠A (exterior angle property)
x° = 50° + 60°
x° = 110°
Also x° + y° = 180°
110°+ y°= 180°
y° = 180° – 110°
y° = 70°
(OR) in ΔMAN,
∠M + ∠A + ∠N = 180° (angle – sum property )
50° + 60° + y° = 180°
110° + y° = 180°
y° = 180°- 110°
∴ y° = 70°
iv) In the figure ΔABC,
x° = 60° (vertically opposite angles)
∠A + ∠B + ∠ACB = 180° (angle – sum property)
y° + 30° + 60° = 180°
y° + 90° = 180°
y° = 180° – 90°
∴ y° = 90°
v) In the figure ΔEFG,
y° = 90° (vertically opposite angles)
Also in ΔEFG;
∠F + ∠E + ∠G = 180° (angle – sum property)
∴ x° + x° + y° = 180
2x° + 90° = 180°
2x° = 180°- 90°
2x° = 90°
x° = 90∘2
∴ x° = 45°
vi) In the figure ΔLET,
∠L = ∠T = ∠E = x° (vertically opposite angles)
Also in ΔLET
∠L + ∠E + ∠T = 180° (angle – sum property)
x° + x° + x° = 180°
3x° = 180°
x° = 180∘3
x° = 60°
Question 3.
Find the measure of the third angle of triangles whose two angles are given below:
(i) 38° , 102°
(ii) 116°, 30°
(iii) 40°, 80°
Solution:
(i) 38° , 102°
Let the third angle be x° then
38° + 102° + x° = 180° (angle – sum property)
140° + x° = 180°
x° = 180° – 140° = 40°
(ii) 116°, 30°
Let the third angle be x°
then 116° + 300 + x° = 180° (angle – sum property)
146° + x = 180°
x= 180°- 146° = 34°
(iii) 40°, 80°
Let the third angle be x° then
40C + 80° + x° = 180° (angle-sum property)
120°+x° = 180°
x° = 180 – 120° – 60°.
Question 4.
In a right-angled triangle, one acute angle is 30°. Find the other acute angle.
Solution:
Given triangle is right angled triangle.
Let the third angle be x°
then 90° +30° + x° = 180° (angle – sum property)
120° + x° – 180°
x° = 180° – 120° = 60°
Question 5.
State true or false for each of the following statements.
(i) A triangle can have two right angles.
(ii) A triangle can have two acute angles.
(iii) A triangle can have two obtuse angles.
(iv) Each angle of a triangle can be less than 60°.
Solution:
(i) A triangle can have two right angles. – False
(ii) A triangle can have two acute angles. – True
(iii) A triangle can have two obtuse angles. – False
(iv) Each angle of a triangle can be less than 60°. – False
Question 6.
The angles of a triangle are in the ratio 1 : 2 : 3. Find the angles.
Solution:
Given that ratio of the angle = 1: 2: 3
Sum of the terms of the ratio – 1 + 2 + 3 = 6
Sum of the angles of a triangle = 1800
∴ 1st angle = 16 x 180° = 30° (angle-sum property)
∴ 2nd angle = 26 x 180° = 60° (angle – sum property)
∴ 3rd angle = 36 x 180° = 90° (angIe – sum property)
Question 7.
In the figure, DE⎯⎯⎯⎯⎯⎯⎯⎯‖BC⎯⎯⎯⎯⎯⎯⎯⎯ , ∠A = 300 and ∠B = 50°. Find the values of x, y and z.
Solution:
y° = 50° (correspondIng angles)
x° = z° (corresponding angles)
Also in MBC;
∠A + ∠B +∠C = 180° (angIe – sum property)
30° + 50° + z° = 180°
80° + z° = 180°
z° = 180° – 80°
∴ z° = 100°
∴ x° = 100°; y° = 50°; z° = 100°
Question 8.
In the figure, ∠ABD = 3 ∠DAB and ∠BDC = 96°. Find ∠ABD.
Solution:
In the figure
∠ABD + ∠DAB = 96° (exterior angle property)
3∠DAB + ∠DAB = 96° (given)
4∠DAB = 96°
∠DAB = 96∘4 = 24°
∠ABD = 3 x 24° = 72°
Question 9.
In ΔPQR ∠P= 2 ∠Q and 2 ∠R =3 ∠Q , calculate the angles of ΔPQR.
Solution:
In ΔPQR
∠P + ∠Q + ∠R = 180° also
∠P:∠Q:∠R = 2∠Q:∠Q: 32∠Q = 4 : 2 : 3
Sum of the term of the ratio = 4 + 2 + 3 = 9
∠P = 49 x 180° = 80°
∠Q = 29 x 180° = 40°
∠R = 39 x 180° = 60°
Question 10.
If the angles of a triangle are in the ratio 1:4: 5, find the angles.
Solution:
Given that ratio of the angles = 1 : 4 : 5
Sum of the terms of the ratio = 1 + 4 + 5 = 10
Sum of the angles 180°
∴ 1st angIe = 110 x 180° = 18°
2nd angle 410 x 180° = 72°
3rd angle = 510 x 180°= 90°
Question 11.
The acute angles of a right triangle are in the ratio 2 : 3. Find the angles of the triangle.
Solution:
Given that ratio of acute angles = 2 : 3
Sum of the terms of the ratio = 2 + 3 = 5
Sum of the acute angles = 90°
∴ 1st acute angle x 900 = 36°
2nd acute angle = x 900 = 540
∴ Angles of the triangle = 36°, 54° and 90°
Question 12.
In the figure, ∆PQR is right angled at Q, ML⎯⎯⎯⎯⎯⎯⎯⎯⎯‖RQ−→− and ∠LMR = 130°. Find ∠LPM, ∠PML and ∠PRQ.
Solution:
∠PRQ + ∠LMR = 180° (int, angles on the same side of the transversal)
∠PRQ + 130° = 18 0°
∴ ∠PRQ = 180° – 130°= 50°
In ∆PRQ,
∠P + ∠R +∠Q = 180° (angle – sum property)
∠LPM + 50° + 90° = 180°
∠LPM + 140° = 180°
∴ ∠LPM = 180° – 140° = 40°
Also ∠PML + ∠LMR = 180° (Linear pair of angles)
∴ ∠PML + 130° = 180°
∠PML = 180° – 130° = 50°
(or) ∠PML = ∠PRQ = 50° (corresponding angles)
Question 13.
In Figure ABCDE, find ∠1 +∠2 + ∠3 + ∠4 + ∠5.
Solution:
In ∆ABC, ∠BAC + ∠ACB + ∠ABC = 180° ………….(1)
In ∆ACD, ∠CAD + ∠ADC + ∠ACD = 180° ……………. (2)
In ∆ADE, ∠DAE + ∠ADE + ∠AED = 180° …………(3)
Adding (1), (2) and (3) we get
(∠BAC + ∠ACB + ∠ABC) + ∠CAD+ (∠ADC + ∠ACD + ∠DAE + ∠ADE + ∠AED = 180°+ 180° 180°
(∠BAC + ∠CAD + ∠DAE) + ∠ABC + (∠ACB + ∠ACD) + ∠ADC + ∠ADE) + ∠AED = 180° + 180° + 180°
Hene
∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 540°
AP Board Textbook Solutions PDF for Class 7th Maths
- AP Board Class 7 Maths Chapter 1 Integers Ex 1
- AP Board Class 7 Maths Chapter 1 Integers Ex 2
- AP Board Class 7 Maths Chapter 1 Integers Ex 3
- AP Board Class 7 Maths Chapter 1 Integers Ex 4
- AP Board Class 7 Maths Chapter 1 Integers Ex 5
- AP Board Class 7 Maths Chapter 1 Integers Ex 6
- AP Board Class 7 Maths Chapter 1 Integers Ex 7
- AP Board Class 7 Maths Chapter 1 Integers InText Questions
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers Ex 1
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers Ex 2
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers Ex 3
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers Ex 4
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers Ex 5
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers Ex 6
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers Ex 7
- AP Board Class 7 Maths Chapter 2 Fractions Decimals and Rational Numbers InText Questions
- AP Board Class 7 Maths Chapter 3 Simple Equations Ex 1
- AP Board Class 7 Maths Chapter 3 Simple Equations Ex 2
- AP Board Class 7 Maths Chapter 3 Simple Equations Ex 3
- AP Board Class 7 Maths Chapter 4 Lines and Angles Ex 1
- AP Board Class 7 Maths Chapter 4 Lines and Angles Ex 2
- AP Board Class 7 Maths Chapter 4 Lines and Angles Ex 3
- AP Board Class 7 Maths Chapter 4 Lines and Angles Ex 4
- AP Board Class 7 Maths Chapter 4 Lines and Angles Ex 5
- AP Board Class 7 Maths Chapter 4 Lines and Angles Ex 6
- AP Board Class 7 Maths Chapter 4 Lines and Angles Ex 7
- AP Board Class 7 Maths Chapter 4 Lines and Angles InText Questions
- AP Board Class 7 Maths Chapter 5 Triangle and Its Properties Ex 1
- AP Board Class 7 Maths Chapter 5 Triangle and Its Properties Ex 2
- AP Board Class 7 Maths Chapter 5 Triangle and Its Properties Ex 3
- AP Board Class 7 Maths Chapter 5 Triangle and Its Properties Ex 4
- AP Board Class 7 Maths Chapter 5 Triangle and Its Properties InText Questions
- AP Board Class 7 Maths Chapter 6 Ratio Applications Ex 1
- AP Board Class 7 Maths Chapter 6 Ratio Applications Ex 2
- AP Board Class 7 Maths Chapter 6 Ratio Applications Ex 3
- AP Board Class 7 Maths Chapter 6 Ratio Applications Ex 4
- AP Board Class 7 Maths Chapter 6 Ratio Applications Ex 5
- AP Board Class 7 Maths Chapter 6 Ratio Applications Ex 6
- AP Board Class 7 Maths Chapter 6 Ratio Applications InText Questions
- AP Board Class 7 Maths Chapter 7 Data Handling Ex 1
- AP Board Class 7 Maths Chapter 7 Data Handling Ex 2
- AP Board Class 7 Maths Chapter 7 Data Handling Ex 3
- AP Board Class 7 Maths Chapter 7 Data Handling Ex 4
- AP Board Class 7 Maths Chapter 7 Data Handling InText Questions
- AP Board Class 7 Maths Chapter 8 Congruency of Triangles Ex 1
- AP Board Class 7 Maths Chapter 8 Congruency of Triangles Ex 2
- AP Board Class 7 Maths Chapter 8 Congruence of Triangles Ex 3
- AP Board Class 7 Maths Chapter 8 Congruency of Triangles Ex 4
- AP Board Class 7 Maths Chapter 8 Congruency of Triangles InText Questions
- AP Board Class 7 Maths Chapter 9 Construction of Triangles Ex 1
- AP Board Class 7 Maths Chapter 9 Construction of Triangles Ex 2
- AP Board Class 7 Maths Chapter 9 Construction of Triangles Ex 3
- AP Board Class 7 Maths Chapter 9 Construction of Triangles Ex 4
- AP Board Class 7 Maths Chapter 9 Construction of Triangles InText Questions
- AP Board Class 7 Maths Chapter 10 Algebraic Expressions Ex 1
- AP Board Class 7 Maths Chapter 10 Algebraic Expressions Ex 2
- AP Board Class 7 Maths Chapter 10 Algebraic Expressions Ex 3
- AP Board Class 7 Maths Chapter 10 Algebraic Expressions Ex 4
- AP Board Class 7 Maths Chapter 10 Algebraic Expressions InText Questions
- AP Board Class 7 Maths Chapter 11 Exponents Ex 1
- AP Board Class 7 Maths Chapter 11 Exponents Ex 2
- AP Board Class 7 Maths Chapter 11 Exponents Ex 3
- AP Board Class 7 Maths Chapter 11 Exponents InText Questions
- AP Board Class 7 Maths Chapter 12 Quadrilaterals Ex 1
- AP Board Class 7 Maths Chapter 12 Quadrilaterals Ex 2
- AP Board Class 7 Maths Chapter 12 Quadrilaterals InText Questions
- AP Board Class 7 Maths Chapter 13 Area and Perimeter Ex 1
- AP Board Class 7 Maths Chapter 13 Area and Perimeter Ex 2
- AP Board Class 7 Maths Chapter 13 Area and Perimeter Ex 3
- AP Board Class 7 Maths Chapter 13 Area and Perimeter Ex 4
- AP Board Class 7 Maths Chapter 13 Area and Perimeter Ex 5
- AP Board Class 7 Maths Chapter 13 Area and Perimeter Ex 6
- AP Board Class 7 Maths Chapter 13 Area and Perimeter InText Questions
- AP Board Class 7 Maths Chapter 14 Understanding 3D and 2D Shapes Ex 1
- AP Board Class 7 Maths Chapter 14 Understanding 3D and 2D Shapes Ex 2
- AP Board Class 7 Maths Chapter 14 Understanding 3D and 2D Shapes Ex 3
- AP Board Class 7 Maths Chapter 14 Understanding 3D and 2D Shapes Ex 4
- AP Board Class 7 Maths Chapter 14 Understanding 3D and 2D Shapes InText Questions
- AP Board Class 7 Maths Chapter 15 Symmetry Ex 1
- AP Board Class 7 Maths Chapter 15 Symmetry Ex 2
- AP Board Class 7 Maths Chapter 15 Symmetry Ex 3
- AP Board Class 7 Maths Chapter 15 Symmetry Ex 4
- AP Board Class 7 Maths Chapter 15 Symmetry InText Questions
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