In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to
a. 40°
b. 80°
c. 120°
d. 50°

Solution:

Given, PQR is a triangle.

Also, PQ = QR

∠Q = 100°

We have to find the value of ∠R.

An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.

Since PQ = QR, ∠P = ∠R

By angle sum property of a triangle,

We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.

∠P + ∠R + ∠Q = 180°

∠P + 100° + ∠P = 180°

2∠P + 100° = 180°

2∠P = 180° - 100°

2∠P = 80°

∠P = 80°/2

∠P = 40°

Therefore, ∠P = ∠Q = 40°

✦ Try This: If two angles of a triangle are 70° each, then the triangle is isosceles but not equilateral. Justify your answer

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 17

In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to: a. 40°, b. 80°, c. 120°, d. 50°

Summary:

In ∆PQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to 40°

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