Angles ABC and DBE are vertical angles where m∠ABC = (5x + 5)° and m∠DBE = (6x − 3)°.

Question

Part A: Solve for x. Show every step of your work.

Part B: Are the vertical angles also complementary angles? Explain.

Answer 1

Part A: Solve for x. Show every step of your work.

Since angles ABC and DBE are vertical angles, they are congruent. Therefore, we can set up the following equation:

5x + 5 = 6x - 3

Simplify the equation by combining like terms:

5 = x - 3

Add 3 to both sides of the equation:

5 + 3 = x

8 = x

Therefore, x = 8.

Part B: Are the vertical angles also complementary angles? Explain.

To determine if the vertical angles are also complementary angles, we need to check if their sum is equal to 90 degrees.

m∠ABC + m∠DBE = (5x + 5) + (6x - 3) = 11x + 2

Substitute x = 8 into the equation:

11(8) + 2 = 90

88 + 2 = 90

90 = 90

The sum of the two angles is equal to 90 degrees. Therefore, the vertical angles in this case are also complementary angles.