Question

2
note: figure not drawn to scale.
in the triangle shown, ( pq = qr ). what is the value of ( x )?
a 141
b 78
c 51
d 39

Explanation:

Step1: Use the property of isosceles triangle

Since \(PQ = QR\), \(\angle P=\angle R\) (angles opposite to equal sides in a triangle are equal).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle P = 39^{\circ}\), \(\angle Q=102^{\circ}\), and \(\angle R=x\).
We know that \(\angle P+\angle Q+\angle R = 180^{\circ}\).
Substitute the values: \(39^{\circ}+102^{\circ}+x=180^{\circ}\).
Simplify the left - hand side: \(141^{\circ}+x = 180^{\circ}\).
Solve for \(x\): \(x=180^{\circ}-141^{\circ}\).

Answer:

D. 39