Question

Point C is in the interior of ∠ABD, and ∠ABC ≅ ∠CBC. If m∠ABC = (5/8x + 18) and m∠CBD = (4x), what is m∠ABD?

Answer 1

Answer:

$\angle ABD =42.4^{\circ}$

Step-by-step explanation:

We are given that Point C is in the interior of ∠ABD

We are also given that ∠ABC ≅ ∠CBD

Now ,

$\angle ABC = (\frac{5}{8}x + 18)\\\angle CBD = (4x)$

Since we are given that ∠ABC ≅ ∠CBD

So, $\frac{5}{8}x + 18=4x\\4x-\frac{5}{8}x=18\\\frac{32x-5x}{8}=18\\\frac{27x}{8}=18\\x=\frac{18 \times 8}{27}\\x=5.3$

$\angle CBD = (4x)=4(5.3)=21.2^{\circ}$

$\angle ABD = \angle CBD+\angle ABC=21.2+21.2=42.4^{\circ}$

Hence $\angle ABD =42.4^{\circ}$