Two intersecting lines create four angles, numbered 1, 2, 3, and 4, where ∠4

Question

is adjacent to ∠1
and ∠3
, and m∠2=110°
. Which other angle has a measure that is also equal to 110°
?

Answer 1

When two lines intersect, they create four angles that are related to each other in specific ways. The angles opposite each other at the intersection are known as vertical angles and are equal. Adjacent angles (angles that share a common side) are supplementary, meaning their measures add up to 180°.

Given that \( m\angle 2 = 110° \):

1. The angle opposite to \( \angle 2 \) is \( \angle 4 \) (since vertical angles are equal). Therefore, \( m\angle 4 = 110° \).

So, the other angle that has a measure equal to \( 110° \) is \( \angle 4 \).