Question

1. if ( mangle 8 = 72^circ ), then ( mangle 9 = ? )

a. ( 72^circ )
b. ( 80^circ )
c. ( 100^circ )
d. ( 108^circ )

1. are ( angle 5 ) and ( angle 6 ) a linear pair, vertical angles, or neither?

a. linear pair
b. vertical angles
c. neither

Explanation:

Question 4

Step1: Identify angle relationship

∠8 and ∠9 are supplementary (form a linear pair), so \( m\angle8 + m\angle9 = 180^\circ \).

Step2: Solve for \( m\angle9 \)

Given \( m\angle8 = 72^\circ \), substitute into the equation: \( m\angle9 = 180^\circ - 72^\circ \).
\( m\angle9 = 108^\circ \).

A linear pair of angles are adjacent and supplementary (sum to \( 180^\circ \)) and form a straight line. ∠5 and ∠6 are adjacent, share a common side, and their non - common sides form a straight line, so they are a linear pair. Vertical angles are opposite each other when two lines intersect, which is not the case here.

Answer:

D. \( 108^\circ \)

Question 5