Question

Anyone know how to do this?! Help!

Answer 1

Given:

Vertical angles.

One angle is 85°.

To find:

The measure of ∠1, ∠2 and ∠3.

Solution:

∠2 and 85° are vertically opposite angles and ∠1 and ∠3 are vertically opposite angles.

Vertical angle theorem:

If two lines are intersecting, then the vertically opposite angles are congruent.

⇒ m∠2 = 85°

Sum of the adjacent angles in a straight line = 180°

m∠2 + m∠3 = 180°

85° + m∠3 = 180°

Subtract 85° from both sides.

85° + m∠3 - 85° = 180° - 85°

m∠3 = 95°

By vertical angle theorem:

⇒ m∠1 = m∠3

⇒ m∠1 = 95°

Therefore m∠1 = 95°, m∠2 = 85° and m∠3 = 95°.