Question

In triangle, P, Q, R, comma△PQR, start overline, Q, R, end overline, \cong, start overline, P, Q, end overline

QR
​
≅
PQ
​
and m, angle, Q, equals, 84, degrees, .m∠Q=84
∘
. Find m, angle, P, .m∠P.

Answer 1

In an isosceles triangle PQR with sides QR congruent to PQ and angle Q measuring 84 degrees, the measure of angle P is calculated to be 48 degrees.

Step-by-step explanation:

In triangle PQR, where sides QR ≅ PQ and the measure of angle Q is given as 84 degrees, we are looking to find the measure of angle P. Since QR is congruent to PQ, we know that triangle PQR is an isosceles triangle, which means the angles opposite the equal sides are also equal. This means that angles P and R are equal. The sum of interior angles in any triangle is 180 degrees.

Therefore, if we subtract the given angle Q from 180 degrees, we will find the sum of angles P and R. Then, since angles P and R are equal, we divide that sum by 2 to find the measure of angle P.

To calculate:

1. Sum of angles P and R = 180 degrees - m∠Q = 180 degrees - 84 degrees = 96 degrees.
2. m∠P = m∠R = 96 degrees / 2 = 48 degrees.

Therefore, the measure of angle P in triangle PQR is 48 degrees.