Angles ABC and DBE are vertical angles where m∠ABC = (5x + 5)° and m∠DBE = (6x − 3)°.
Part A: Solve for x. Show every step of your work.
Part B: Are the vertical angles also complementary angles? Explain.
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.