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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