In Fig. 6.33, find the measures of ∠x and ∠y.

Solution:

Given, the figure represents a triangle.

We have to find the values of ∠x and ∠y.

Consider triangle ABC,

Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.

By angle sum property,

∠A + ∠B + ∠C = 180°

45° + 60° + ∠x = 180°

105° + ∠x = 180°

∠x = 180° - 105°

∠x = 75°

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.

∠y = ∠x + 60°

∠y = 75° + 60°

∠y = 135°

Therefore, the values of ∠x and ∠y are 75° and 135°.

✦ Try This: Find the value of y.

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

---

NCERT Exemplar Class 7 Maths Chapter 6 Problem 116

In Fig. 6.33, find the measures of ∠x and ∠y.

Summary:

In Fig. 6.33, the measures of ∠x and ∠y are 75° and 135°.

---

☛ Related Questions:

• In Fig. 6.34, find the measures of ∠PON and ∠NPO
• In Fig. 6.35, QP || RT. Find the values of x and y
• Find the measure of ∠A in Fig. 6.36