# In Fig. 6.34, find the measures of ∠PON and ∠NPO.

**Solution:**

Given, the figure represents two triangles LMO and PNO.

We have to find the measure of ∠PON and ∠NPO.

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

∠LMO + ∠MOL + ∠MLO = 180°

20° + ∠MOL + 70° = 180°

∠MOL + 90° = 180°

∠MOL = 180° - 90°

∠MOL = 90°

We know that vertically opposite angles are equal.

So, ∠MOL = ∠PON

∠PON = 90°

By angle sum property,

∠PNO + ∠OPN + ∠PON = 180°

70° + ∠NPO + 90° = 180°

∠NPO + 160° = 180°

∠NPO = 180° - 160°

∠NPO = 20°

Therefore, the values of ∠PON and ∠NPO are 90° and 20°.

**✦ Try This: **Find the value of x.

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

**NCERT Exemplar Class 7 Maths Chapter 6 Problem 117**

## In Fig. 6.34, find the measures of ∠PON and ∠NPO.

**Summary:**

In Fig. 6.34, the measures of ∠PON and ∠NPO are 90° and 20°.

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