Answer: m∠ABD = 24°, m∠CBD = 24°, and m∠ABC = 48°
Explanation:
Since BD is a bisector, this means that ∠ABD and ∠DBC are congruent. We can use this information to help us solve for x.
Given:
∠ABD = ∠DBC
Substitute:
3x + 6 = 7x - 18
Subtract 6 and 7x from both sides of the equation:
4x - 7x = -18 - 6
-4x = -24
Divide both sides of the equation by -4:
x = 6
Using this value of x, we can find all three of the angle measurements. m∠ABD and m∠CBD will have the same measurement since they are congruent based on the bisector, but I will still show up working out both.
m∠ABD = 3x + 6 = 3(6) + 6 = 18 + 6 = 24°
m∠CBD = 7x - 18 = 7(6) - 18 = 42 - 18 = 24°
m∠ABC = m∠ABD + m∠CBD = 24 + 24 = 48°