Question

find the measure of each numbered angle.
m∠1 = \boxed{\space}°, m∠2 = \boxed{\space}°, m∠3 = \boxed{\space}°
(image of two triangles with vertices p, m, q and o, n, q; angles at p: 58°, at m: 66°; angle at o: 50°; angles 1, 2, 3 at q and in the lower triangle)

Explanation:

Step1: Find \( m\angle1 \)

In triangle \( PMQ \), the sum of interior angles is \( 180^\circ \). So \( m\angle1 = 180^\circ - 58^\circ - 66^\circ \). Calculating: \( 180 - 58 - 66 = 56^\circ \).

Step2: Find \( m\angle2 \)

\( \angle1 \) and \( \angle2 \) are vertical angles, so they are equal. Thus \( m\angle2 = m\angle1 = 56^\circ \).

Step3: Find \( m\angle3 \)

In triangle \( ONQ \), the sum of interior angles is \( 180^\circ \). So \( m\angle3 = 180^\circ - m\angle2 - 50^\circ \). Substituting \( m\angle2 = 56^\circ \), we get \( 180 - 56 - 50 = 74^\circ \).

Answer:

\( m\angle1 = 56^\circ \), \( m\angle2 = 56^\circ \), \( m\angle3 = 74^\circ \)