Question

The measure of ∠CBD is 45% of the measure of ∠ABC. Find the value of x.

Answer 1

Explanation:

Hello! Remember you have to write complete questions in order to get good and exact answers. Here we have no expressions for ∠CBD and ∠ABC, so I'll assume:

$\angle CBD=15x-24 \\ \\ \angle ABC=20x+40$

We know that the measure of ∠CBD is 45% of the measure of ∠ABC, then:

$\angle CBD = 45\%(\angle ABC) \\ \\ \\ Or: \\ \\ \angle CBD = 0.45(\angle ABC) \\ \\ \\ Substituting \ expressions: \\ \\ 15x-24=0.45(20x+40) \\ \\ \\ Solving \ for \ x: \\ \\ 15x-24=9x+18 \\ \\ 15x-9x=24+18 \\ \\ 6x=42 \\ \\ x=\frac{42}{6} \\ \\ \boxed{x=7}$