Question

1. ( mangle r ) 4.1

(image of a right triangle ( \triangle pqr ) with right angle at ( p ), ( angle q ) labeled ( x^circ ), vertices ( q ), ( p ), ( r ))

Explanation:

Step1: Use the sum of angles in a triangle

The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle PQR\), \(\angle P = 90^{\circ}\), \(\angle Q=x^{\circ}\), and \(\angle R\) is what we need to find. Let \(m\angle R = y^{\circ}\). Then \(90 + x+y=180\).

Step2: Solve for \(y\)

Subtract \(90 + x\) from both sides of the equation \(90 + x+y=180\). We get \(y = 90 - x\).

Answer:

\(m\angle R=(90 - x)^{\circ}\)