Question

Angles ABC and DBE are vertical angles where m∠ABC = (8x + 3)° and m∠DBE = (9x − 2)°. Part A: Solve for x. Show every step of your work. (2 points) Part B: Are the vertical angles also complementary angles? Explain. (2 points)

Answer 1

x=5

The angles are not complimentary

Explanation:

Part A.

Vertical angles are congruent, therefore m∠ABC≅m∠DBE.

If m∠ABC≅m∠DBE, then (8x+3)=(9x-2).

Solve the equation

8x+3=9x-2

8x-9x=-2-3

-x=-5

x=5

Part B.

The definition of complimentary angles is that complimentary angles add up to 90°.

First lets find the measures of these angles, so just put 5 in for x.

m∠ABC=8(5)+3

m∠ABC=40+3

m∠ABC=43

We know that the angles are congruent, so m∠DBE=43

43+43≠90, so the angles are not complimentary.