Question

What is the measure of the indicated angle ?

Answer 1

Answer:

The measure of the indicated angle is 72°

Step-by-step explanation:

If two parallel lines intersected by a transversal, then

• There are pairs of corresponding angles equal in measures

• There are pairs of alternate interior angles equal in measures

• There are pairs of alternate exterior angles equal in measures

• There are pairs of adjacent interior angles that are supplementary

In the given figure

∵ There are two parallel lines intersected by a transversal

∵ The angle of measure 108° and the indicated angle are adjacent

   interior angles

∴ They are supplementary

∵ The sum of the measures of supplementary angles is 180°

∴ 108 + indicated angle = 180

→ Subtract 108 from both sides

∴ The measure of the indicated angle = 72°