Question

use the figure shown.
if ( mangle 4 = 96 ) and ( mangle 5 = 138 ), what is ( mangle 3 )?
a. 42
b. 54
c. 84
d. 96

Explanation:

Step1: Find m∠1

∠4 and ∠1 are supplementary (linear pair), so \( m\angle1 = 180^\circ - m\angle4 \).
\( m\angle1 = 180^\circ - 96^\circ = 84^\circ \)

Step2: Find m∠2

∠5 and ∠2 are supplementary (linear pair), so \( m\angle2 = 180^\circ - m\angle5 \).
\( m\angle2 = 180^\circ - 138^\circ = 42^\circ \)

Step3: Find m∠3

In a triangle, the sum of angles is \( 180^\circ \), so \( m\angle3 = 180^\circ - m\angle1 - m\angle2 \).
\( m\angle3 = 180^\circ - 84^\circ - 42^\circ = 54^\circ \)

Answer:

B. 54