In Fig. 5.22, the value of a is
a. 20°
b. 15°
c. 5°
d. 10°
Solution:
Given, the figure represents three lines AD, CF and BE which intersect each other at O.
We have to find the value of a.
Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
From the figure,
∠AOF = ∠COD
Given, ∠AOF = 90°
So, ∠COD = 90°
We know that the sum of all angles lying on a straight line is always equal to 180 degrees.
Considering line BE and rays OC and OD,
So, ∠BOC + ∠COD + ∠EOD = 180°
40° + 90° + 5a = 180°
130° + 5a = 180°
5a = 180° - 130°
5a = 50°
a = 50°/5
Therefore, a = 10°
✦ Try This: In the given figure, write down each pair of alternate interior angles.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 26
In Fig. 5.22, the value of a is: a. 20°, b. 15°, c. 5°, d.10°
Summary:
In Fig. 5.22, the value of a is 10°
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