Question

In the diagram of ABC below, AB is extended to point D.с(3x + 10)(x + 40°|(x)"BADIf mZCAB = x + 40, mZACB = 3x + 10, mZCBD = 6x, what is mZCAB?

Answer 1

m∠CAB = 65°

Step-by-step explanation:

m∠CAB = x + 40, m∠ACB = 3x + 10, m∠CBD = 6x

∠C + ∠A + ∠B = 180 degrees (sum of angles in a triangle)

∠CAB + ∠CBD = 180 degrees (angles on a straight line)

∠CAB = 180 - ∠CBD

∠CAB = 180 - 6x

m∠CAB + m∠ACB + ∠CAB = 180

x + 40 + 3x + 10 + 180 - 6x = 180

collect like terms:

x + 3x - 6x + 40 + 10 + 180 = 180

-2x + 230 = 180

-2x = 180 -230

-2x = -50

Divide both sides by -2:

-2x/-2 = -50/-2

x = 25

m∠CAB = x + 40 = 25 + 40

m∠CAB = 65°