Question

AB is the bisector of CAD. If the mCAB = 2x+30 and m DAB=5x+12 what is the mCAB

Answer 1

Answer:

$CAB = 42$

Step-by-step explanation:

Given

$CAB = 2x + 30$

$DAB = 5x + 12$

Bisector: AB

Required

Find CAB

Since AB bisects CAD, then

$CAB = DAB$

This is so because AB divides CAD into two equal parts which are CAB and DAB

$CAB = DAB$

Substitute values for CAB and DAB

$2x + 30 = 5x + 12$

Collect Like Terms

$2x- 5x = 12 - 30$

$-3x = -18$

Divide both sides by -3

$x = 6$

To solve for CAB, we simply substitute 6 for x in $CAB = 2x + 30$

$CAB = 2 * 6 + 30$

$CAB = 12 + 30$

$CAB = 42$