Question

Angle GNH is congruent to angle KNL. Angle MNL is complementary to angle KNL. What is the measure of angle MNL?

42°
48°
132°
138°

Answer 1

The measure of angle MNL is
`42\°`

Explanation:

see the attached figure to better understand the problem

In this problem we know that

angle GNH is congruent to angle KNL

`m<GNH=m<KNL` -----> by vertical angles

`m<GNH=48\°`

so

`m<KNL=48\°`

Find the measure of angle MNL

`m<MNL+m<KNL=90\°` ------> by complementary angles

Substitute and solve for m<MNL

`m<MNL+48\°=90\°`

`m<MNL=90\°-48\°=42\°`