In Fig. 6.5, find x and y

Solution:

Given, the figure represents a triangle ABC

We have to find the values of x and y.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.

Considering triangle ABD,

∠ABD = x

By exterior angle property,

∠ABD = ∠DBA + ∠BAD

= 60° + 30°

x = 90°

Considering triangle ABC,

∠XAC = y

By exterior angle property,

∠XAC = ∠ABC + ∠ACB

= 60° + 45°

y = 105°

Therefore, the values of x and y are 90° and 105°.

✦ Try This: In the given figure, measures of some angles are given. Using the measures find the values of x, y, z

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Sample Problem 13

In Fig. 6.5, find x and y

Summary:

In Fig. 6.5, the values of x and y are 90° and 105°

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