Answer:
B. 110°
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Given:
- m∠9 = 110°
- m∠8 = 70°
- p || q
Apply the Vertical Angle Theorem to find the measure of angle 8:
⇒ m∠3 = m∠8 = 70°
As angles 7 and 8 form a linear pair:
⇒ m∠7 + m∠8 = 180°
⇒ m∠7 + 70° = 180°
⇒ m∠7 = 110°
As line p is parallel to line q, apply the Corresponding Angles Postulate to find the measure of angle 15:
⇒ m∠15 = m∠7 = 110°
Therefore, the measure of angle 15 is 110°.
