Question

Point C is in the interior of ∠ABD, and ∠ABC ≅ ∠CBD. If m∠ABC = 5/2x + 18) and m∠CBD = (4x), what is m∠ABD?

Answer 1

Answer:

m∠ABD = 96

Step-by-step explanation:

Given

m∠ABC = 5/2x + 18

m∠CBD = 4x

Required

Determine m∠ABD

From the given parameters, we understand that:

∠ABC ≅ ∠CBD

This implies that:

$\frac{5}{2}x + 18 = 4x$

Collect Like Terms

$\frac{5}{2}x - 4x =- 18$

Take LCM

$\frac{5x - 8x}{2} = -18$

$\frac{-3x}{2} = -18$

Cross Multiply

$-3x = -18 * 2$

$-3x = -36$

Divide through by -3

$x = 12$

m∠ABD can be calculated using:

m∠ABD = m∠ABC + m∠CBD

$ABD = \frac{5}{2}x + 18 + 4x$

Substitute 12 for x

$ABD = \frac{5}{2} * 12 + 18 + 4 * 12$

$ABD = 30 + 18 + 48$

$ABD = 96$

Hence;

m∠ABD = 96