Question

In the accompanying diagram, CAB is parallel to DOG, AO is a transversal, the

mACAO = 2x and the mDOA = 3x + 40. Find the maCAO.

Answer 1

∠ CAO = 56°

Explanation:

∠ CAO and ∠ DOA are same- side interior angles and sum to 180° , so

∠ CAO + ∠ DOA = 180 , that is

2x + 3x + 40 = 180

5x + 40 = 180 ( subtract 40 from both sides )

5x = 140 ( divide both sides by 5 )

x = 28

Then

∠ CAO = 2x = 2 × 28 = 56°