Question

applying the polygon exterior angle sum theorem
what is the measure of angle acb?
108°
145°

Explanation:

Step1: Find the interior angles at A and B

• For angle at A:

The exterior angle at A is \(108^{\circ}\). Using the linear - pair relationship (interior + exterior = \(180^{\circ}\)), the interior angle \(\angle CAB=180 - 108=72^{\circ}\)

• For angle at B:

The exterior angle at B is \(145^{\circ}\). Using the linear - pair relationship, the interior angle \(\angle ABC = 180-145 = 35^{\circ}\)

Step2: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle \(\triangle ABC\) is \(180^{\circ}\). Let \(\angle ACB=x\).
By the formula \(\angle CAB+\angle ABC+\angle ACB = 180^{\circ}\)
Substitute \(\angle CAB = 72^{\circ}\) and \(\angle ABC=35^{\circ}\) into the formula: \(72 + 35+x=180\)
Simplify the left - hand side: \(107+x=180\)
Solve for \(x\): \(x=180 - 107\)

Answer:

\(73\)