Question

Suppose BD bisects ABC. If m ABD = 12x+24 and m DBC = 20x +16 what is m ABC?

Answer 1

The measure of ABC is 72

Explanation:

if the angle ABC is bisected, it means that the two angles ABD and DBC are equal;

Thus;

12x + 24 = 20x + 16

20x -12x = 24-16

8x = 8

x = 1

The measure of angle ABC is the sum of the two angles

ABC = 12x + 24 + 20x + 16

ABC = 32x + 40

Substitute x = 1

ABC = 32(1) + 40

ABC = 72 degrees