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, \(73^{\circ}\)
