Question

A, B, and C are collinear, and point B lies in between point A and point C. Point D is a point not on the line. Given that measure of angle ABD = (8x - 2) degrees and measure of angle CBD = (5x) degrees, find measure of angle CBD.

Answer 1

The measure of angle CBD is 70 degrees.

Explanation:

Given that A, B, and C are collinear (on a straight line) and B is in between A and C.

For a point D not on the line:

`\angle ABD+\angle CBD=180^\circ $ (By the Linear Postulate)\\(8x-2)^\circ+5x^\circ=180^\circ\\8x+5x=180^\circ+2^\circ\\13x=182^\circ\\$Divide both sides by 13\\x=14^\circ`

Therefore, the measure of angle CBD

= 5 X 14

`=70^\circ`

The measure of angle CBD is 70 degrees.