Question

the figure shows two intersecting lines.
a) write an equation to show how m∠1 and m∠2 are related.
m∠1 + m∠2 = 180°
when the measures of two angles sum to 180° they are supplementary. ∠1 and ∠2 are supplementary angles.
m∠1 = 137°, find m∠2.
m∠2 =

Explanation:

Step1: Recall the supplementary angle formula

We know that for supplementary angles, \( m\angle1 + m\angle2 = 180^\circ \).

Step2: Substitute \( m\angle1 = 137^\circ \) into the formula

Substitute the given value of \( m\angle1 \) into the equation: \( 137^\circ + m\angle2 = 180^\circ \).

Step3: Solve for \( m\angle2 \)

To find \( m\angle2 \), we subtract \( 137^\circ \) from both sides of the equation: \( m\angle2 = 180^\circ - 137^\circ \).
Calculate the right - hand side: \( 180 - 137 = 43 \), so \( m\angle2 = 43^\circ \).

Answer:

\( 43^\circ \)