Question

find the value of m.

m + 20°
100°

a 80°
b 60°
c 120°
d 140°

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So \( m + 20^\circ = 100^\circ \) is incorrect? Wait, no, wait. Wait, when two lines intersect, vertical angles are equal. Wait, the angle \( m + 20^\circ \) and \( 100^\circ \) are vertical angles? Wait, no, maybe they are supplementary? Wait, no, when two lines intersect, adjacent angles are supplementary, vertical angles are equal. Wait, looking at the diagram, the two angles \( m + 20^\circ \) and \( 100^\circ \) are vertical angles? Wait, no, maybe I made a mistake. Wait, no, vertical angles are opposite each other when two lines cross. So if two lines intersect, the vertical angles are equal. So \( m + 20^\circ = 100^\circ \)? Wait, no, that would give \( m = 80^\circ \), but let's check. Wait, no, maybe they are supplementary? Wait, no, adjacent angles are supplementary. Wait, maybe the angle \( m + 20^\circ \) and \( 100^\circ \) are vertical angles, so they are equal. So \( m + 20^\circ = 100^\circ \), then \( m = 100^\circ - 20^\circ = 80^\circ \)? Wait, but option A is \( 80^\circ \). Wait, but let's re-examine. Wait, maybe the angles are supplementary? Wait, no, vertical angles are equal. Wait, maybe the diagram is such that \( m + 20^\circ \) and \( 100^\circ \) are vertical angles, so they are equal. So solving \( m + 20 = 100 \), subtract 20 from both sides: \( m = 100 - 20 = 80 \). So \( m = 80^\circ \), which is option A.

Step2: Solve for m

Given \( m + 20^\circ = 100^\circ \) (since vertical angles are equal), subtract \( 20^\circ \) from both sides:
\( m = 100^\circ - 20^\circ = 80^\circ \)

Answer:

A. \( 80^\circ \)