Question

1. triangles mno and pqr are similar.

find the measure of the missing angle.
m∠q = degrees

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Use similarity (or angle sum)

For \(\triangle PQR\), we know two angles: \(m\angle P = 62^\circ\), \(m\angle R = 46^\circ\). Let \(m\angle Q = x\). Then \(x + 62^\circ + 46^\circ = 180^\circ\).

Step3: Solve for \(x\)

\(x = 180^\circ - 62^\circ - 46^\circ = 72^\circ\). Also, since triangles are similar, corresponding angles are equal. In \(\triangle MNO\), \(m\angle N = 72^\circ\), so \(m\angle Q\) (corresponding to \(\angle N\)) is \(72^\circ\).

Answer:

\(72\)