Question

What is the measure of angle ACB?

Answer 1

Answer:

Linear pair is a pair of adjacent angles formed when two lines intersect.

so, $\angle EAB$ and $\angle CAB$ are linear pairs.

Linear pairs are always supplementary.

therefore,

$\angle EAB+\angle CAB=180^{\circ}$              ......[1]

Also, it is given in figure, $\angle EAB = 108^{\circ}$

Substitute in [1], we get;

$108^{\circ}+\angle CAB=180^{\circ}$

Simplify:

$\angle CAB =180^{\circ}-108^{\circ}=72^{\circ}$

Exterior- Angle sum Property states that if the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.

then by Exterior angle sum property ;

$\angle ACB+\angle CAB =\angle CBF$

Substitute the values given in the figure;

$\angle ACB+72^{\circ}=145^{\circ}$

simplify;

$\angle ACB =145-72 = 73^{\circ}$

therefore, the measure of angle ACB is, $73^{\circ}$

Answer 2

The answer is 73 degrees.... A triangle adds up to 180 degrees. The angle next  to  B is a supplementary angle so you subtract 180 - 145= 35.... angle next to A is also supplementary so you 180 - 108 = 72

72 + 35 = 107
180 - 107= 73

Your answer is 73 degrees