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

`\angle ABD =42.4^(\circ)`

Explanation:

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

We are also given that ∠ABC ≅ ∠CBD

Now ,

`\angle ABC = ((5)/(8)x + 18)\\\angle CBD = (4x)`

Since we are given that ∠ABC ≅ ∠CBD

So,
`(5)/(8)x + 18=4x\\4x-(5)/(8)x=18\\(32x-5x)/(8)=18\\(27x)/(8)=18\\x=(18 * 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)`