Question

what is the measure of angle acb?

Explanation:

Step1: Find the measure of ∠CAB

Since ∠EAB = 108°, and ∠CAB + ∠EAB = 180° (linear - pair of angles), then ∠CAB=180° - 108° = 72°.

Step2: Find the measure of ∠ABC

Since ∠FBC = 145°, and ∠ABC+∠FBC = 180° (linear - pair of angles), then ∠ABC = 180° - 145°=35°.

Step3: Use the triangle - angle sum theorem

In △ABC, we know that ∠CAB+∠ABC + ∠ACB=180° (triangle - angle sum theorem: the sum of interior angles of a triangle is 180°).
Substitute ∠CAB = 72° and ∠ABC = 35° into the formula: 72°+35°+∠ACB = 180°.
Then ∠ACB=180°-(72° + 35°)=180° - 107° = 73°.

Answer:

73