Answer:
Linear pair is a pair of adjacent angles formed when two lines intersect.
so, [tex]\angle EAB[/tex] and [tex]\angle CAB[/tex] are linear pairs.
Linear pairs are always supplementary.
therefore,
[tex]\angle EAB+\angle CAB=180^{\circ}[/tex] ......[1]
Also, it is given in figure, [tex]\angle EAB = 108^{\circ}[/tex]
Substitute in [1], we get;
[tex]108^{\circ}+\angle CAB=180^{\circ}[/tex]
Simplify:
[tex]\angle CAB =180^{\circ}-108^{\circ}=72^{\circ}[/tex]
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 ;
[tex]\angle ACB+\angle CAB =\angle CBF[/tex]
Substitute the values given in the figure;
[tex]\angle ACB+72^{\circ}=145^{\circ}[/tex]
simplify;
[tex]\angle ACB =145-72 = 73^{\circ}[/tex]
therefore, the measure of angle ACB is, [tex]73^{\circ}[/tex]
