Question

Given:

m∠ABD = 3x + 20
m∠CBD = 6x - 16

What is the measure of angle ∠ABD if line BD bisects ∠ABC?

A) 52 degrees
B) 68 degrees
C) 84 degrees
D) 100 degrees

Answer 1

To find the measure of angle ABD, set up an equation using the fact that line BD bisects angle ABC. Solve for x and substitute it into the equation. The measure of angle ABD is 56 degrees.

Step-by-step explanation:

To find the measure of angle ABD, we can use the fact that line BD bisects angle ABC. This means that angle ABD and angle CBD are congruent. So we can set up an equation:

m∠ABD = m∠CBD

3x + 20 = 6x - 16

Combine like terms: 20 + 16 = 6x - 3x

36 = 3x

Divide both sides by 3: x = 12

Now substitute the value of x back into the equation:

m∠ABD = 3(12) + 20

m∠ABD = 36 + 20

m∠ABD = 56

Therefore, the measure of angle ABD is 56 degrees. So the correct answer is D) 100 degrees.