Question

In the diagram shown below is it given (known) that FB and EH intersect at A and ZEAG is right. Give

two different angles that are both supplementary to ZFAH. What must be true of these two angles?

Answer 1

<HAB is congruent with <FAE

NO CAP

Answer 2

Angle HAB and Angle FAE are congruent angles

Explanation:

we know that

Two angles are supplementary if their sum is equal to 180 degrees

In this problem

m∠FAH+m∠HAB=180° ----> by a linear pair

Remember that

A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. A linear pair of angles must add up to 180 degrees

m∠FAH+m∠FAE=180° ----> by a linear pair

therefore

m∠HAB=m∠FAE -----> by vertical angles

Angle HAB and Angle FAE are congruent angles