Answer:
The measure of angle C is 80 degree.
Step-by-step explanation:
Given information: In ΔABC, ∠A = 40° and ∠B = 60°.
Draw the auxiliary line BD parallel to the line segment AC.
If a transversal line intersects the pair of parallel line, then the alternate interior angles are same.
The angle 1 and 2 are alternate interior angles of angle A and B respectively. Therefore angle 1 is equal to angle A and angle 2 is equal to angle C.
Angle 1,2 and B are supplementary angles because they lie on a straight line, therefore their sum is 180 degree.
[tex]\angle 1+\angle B+\angle 3=180^{\circ}[/tex]
[tex]\angle A+\angle B+\angle =180^{\circ}[/tex]
[tex]40^{\circ}+60^{\circ}+\angle C=180^{\circ}[/tex]
[tex]\angle C=180^{\circ}-100^{\circ}[/tex]
[tex]\angle C=80^{\circ}[/tex]
The angle sum property is another way to solve this problem.
According to the angle sum property, the sum of interior angles of a triangle is 180 degree.
Therefore the measure of angle C is 80 degree.
