Question

the figure shows three intersecting lines. lines g and h are perpendicular.

1. how are ∠1 and ∠2 related?

complete the equation.
m∠1 + m∠2 = 90°

1. when the measures of two angles sum to 90,

they are complementary. ∠1 and ∠2 are
complementary angles.

1. m∠1 = 55°. what is m∠2?

m∠2 = 35
m∠1 + m∠2 = 90°

Explanation:

Step1: Use the complementary angles formula

Since \(\angle1\) and \(\angle2\) are complementary, \(m\angle1 + m\angle2=90^{\circ}\).

Step2: Solve for \(m\angle2\)

Given \(m\angle1 = 55^{\circ}\), substitute into the formula: \(m\angle2=90^{\circ}-m\angle1\).

$$m\angle2 = 90^{\circ}- 55^{\circ}$$

$$m\angle2=35^{\circ}$$

Answer:

\(m\angle2 = 35^{\circ}\)