EXAMPLE 1 Finding an Angle Measure

1 and 2 are complementary, and m 2 = 32. Find m 1.

SOLUTION

m 1+ m 2 = 90

32m 1+ = 90

m 1 = 58

Definition of complementary angles

Subtract 32 from each side.

Substitute 32 for m 2.

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

1. m 1 = 79

m 2 = 101

SOLUTION

m 1+ m 2

= 79° + 101°

ANSWER

Hence, the angles are supplementary.

= 180

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

2. m 1 = 64

m 1 = 36

SOLUTION

m 1+ m 2

= 100°

= 64 + 36

ANSWER

Hence, 1 and 2 are neither complementary nor supplementary.

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

3. m 1 = 52

m 1 = 38

SOLUTION

m 1+ m 2

= 52 + 38

= 90

ANSWER

Hence, 1 and 2 are complementary.

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

4. m 1 = 44

m 1 = 46

SOLUTION

m 1+ m 2

= 90

ANSWER

Hence, 1 and 2 are complementary.

= 44 + 46

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

5. m 1 = 53

m 1 = 47

SOLUTION

m 1+ m 2

= 100

= 53 + 47

ANSWER

Hence, 1 and 2 are neither complementary nor supplementary.

GUIDED PRACTICE for Example 1

Tell whether 1 and 2 are complementary, supplementary, or neither.

6. m 1 = 95

m 1 = 85

SOLUTION

m 1+ m 2

= 180

= 95 + 85

ANSWER

Hence, the angles are supplementary.