Question

Move words to the blanks and equations to the boxes to prove that vertical angles 21 and 23 are congruent.

Because linear pairs of angles are

and

Because angles that are

to the same angle are

it can be concluded that 21 23.

congruent

m21 +m22 = 180°

supplementary

m22 + m23 = 180°

m2l + m23 = 180°

Answer 1

Because linear pairs of angles are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.

Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.

Explanation:

The correct question is attached.

Linear pairs angles are angles which are formed from the intersection of two lines and they are adjacent to each other. Linear pair angles are supplementary.

If angles are supplementary to the same angle, then they are congruent.

∠1 and ∠3 are vertical angles

∠1 and ∠2 form linear pairs while ∠2 and ∠3 form linear pairs. Therefore:

m∠1 + m∠2 = 180° (linear pair angles are supplementary)

m∠2 + m∠3 = 180° (linear pair angles are supplementary)

Hence using transitive property of equality:

m∠1 + m∠2 = m∠2 + m∠3

Using subtraction property of equality by subtracting m∠2 from both sides gives:

m∠1 = m∠3

∠1 ≅ ∠3 (vertical angles are congruent)

Because linear pairs of angles are supplementary. m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°.

Because angles that are supplementary to the same angle are congruent. It can be concluded that ∠1 ≅ ∠3.