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

To solve for x, set the measure of angle ABC equal to the measure of angle DBE and solve for x. The vertical angles ABC and DBE are not complementary angles.

Step-by-step explanation:

Part A:

To solve for x, we set the measure of angle ABC equal to the measure of angle DBE:
(8x + 3)° = (9x - 2)°

Next, we solve for x by isolating the variable:
8x + 3 = 9x - 2
Subtract 8x from both sides:
3 = x - 2
Add 2 to both sides:
5 = x

Therefore, x = 5.

Part B:

No, the vertical angles ABC and DBE are not complementary angles. Complementary angles are two angles that add up to 90 degrees. Vertical angles are formed by the intersection of two lines, and they are always congruent (have the same measure), but they do not have to add up to 90 degrees.