Geometry 10th grade

Question

BD bisects <ABC. Solve for x and find m<ABC. m<ABD=3x+20, m<CBD=6x-16

Answer 1

If BD bisects <ABC then m<ABD is equal to m<CBD (bisects means to cut exactly in half).

Put the expressions for these two angles equal to each other, and then solve for x:

3x + 20 = 6x - 16

-3x = - 36

x = 12

Plug this into one of the expressions: m<ABD = 3(12) + 20 = 56

You will get the same answer for the other angle: m<CBD = 6(12) - 16 = 56

Therefore, the total m<ABC = 56 + 56 = 112