Question

In triangle PQR, r2 = p2 + q2.

Triangle PQR has sides p, q, r opposite to the corresponding vertices P, Q, R

Which equation is true about the measure of the angles of the triangle?

The measure of angle PRQ is equal to 100 degrees
The measure of angle PRQ is equal to 90 degrees
The measure of angle PQR plus the measure of angle QPR is equal to 80 degrees
The measure of angle PQR plus the measure of angle QPR is equal to 70 degrees

Answer 1

the measure of angle PRQ = 90 degrees

Answer 2

Answer: The measure of ∠PRQ is equal to 90 degrees.

Explanation:

Given: In triangle PQR,

`r^2=p^2+q^2`

By converse of Pythagoras theorem,

Δ PQR must be a right triangle.

And in right triangle, the angle opposite to the longest side is right angle.

Therefore, ∠PRQ=90°

∴ The measure of ∠PRQ is equal to 90 degrees.

• The converse of Pythagoras theorem says that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.