Angle ABC and Angle DBE are vertical angles. Angle ABC measures (7x - 5) degrees and Angle DBE measures -2(x - 11) degrees. What is the measure of Angle DBE?

Answer 1

Vertical angles are always congruent, which means they have the same measure. Therefore, we can set the expressions for Angle ABC and Angle DBE equal to each other:

7x - 5 = -2(x - 11)

Now, let's solve for x:

7x - 5 = -2x + 22
7x + 2x = 22 + 5
9x = 27
x = 3

Now that we have found the value of x, we can substitute it back into the expression for Angle DBE to find its measure:

Angle DBE = -2(3 - 11)
Angle DBE = -2(-8)
Angle DBE = 16

Therefore, the measure of Angle DBE is 16 degrees.