In ∆PQR of Fig. 6.32, PQ = PR. Find the measures of ∠Q and ∠R.
Solution:
Given, PQR is a triangle
Also, PQ = PR
We have to find the measure of ∠Q and ∠R.
An isosceles triangle is a triangle that has two sides of equal length.
The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.
Since PQ = PR, PQR is an isosceles triangle.
∠Q and ∠R are apex angles.
In an isosceles triangle, the side opposite the vertex angle is called the base and base angles are equal.
So, ∠Q = ∠R
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,
∠P + ∠Q + ∠R = 180°
30° + ∠Q + ∠R = 180°
30° + 2∠Q = 180°
2∠Q = 180° - 30°
2∠Q = 150°
∠Q = 150°/2
∠Q = 75°
Therefore, ∠Q = ∠R = 75°
✦ 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 115
In ∆PQR of Fig. 6.32, PQ = PR. Find the measures of ∠Q and ∠R.
Summary:
In ∆PQR of Fig. 6.32, PQ = PR. The measures of ∠Q and ∠R are 75° and 75°.
☛ Related Questions: