Angle Relationships: Complementary and Supplementary Worksheet

Question 1

Two angles are complementary. One angle measures 35 degrees. What is the measure of the other angle?

Accepted Answer

The other angle measures 55 degrees because complementary angles add to 90 degrees, and 90 - 35 = 55.

Question 2

Two angles are supplementary. One angle measures 112 degrees. What is the measure of the other angle?

Accepted Answer

The other angle measures 68 degrees because supplementary angles add to 180 degrees, and 180 - 112 = 68.

Question 3

Angles A and B are complementary. Angle A measures 27 degrees. Write and solve an equation to find the measure of angle B.

Accepted Answer

The equation is 27 + B = 90. Subtracting 27 from both sides gives B = 63, so angle B measures 63 degrees.

Question 4

Angles C and D are supplementary. Angle C measures 49 degrees. Write and solve an equation to find the measure of angle D.

Accepted Answer

The equation is 49 + D = 180. Subtracting 49 from both sides gives D = 131, so angle D measures 131 degrees.

Question 5

An angle measures 64 degrees. Is its complement or its supplement larger? Find both angle measures and explain.

Accepted Answer

The complement is 26 degrees because 90 - 64 = 26. The supplement is 116 degrees because 180 - 64 = 116. The supplement is larger.

Question 6

An angle and its complement have equal measures. What is the measure of each angle?

Accepted Answer

Each angle measures 45 degrees because complementary angles add to 90 degrees, and 90 divided by 2 is 45.

Question 7

An angle and its supplement have equal measures. What is the measure of each angle?

Accepted Answer

Each angle measures 90 degrees because supplementary angles add to 180 degrees, and 180 divided by 2 is 90.

Question 8

Two angles form a straight line. One angle measures 73 degrees. What is the measure of the other angle, and what relationship do the angles have?

Accepted Answer

The other angle measures 107 degrees because angles that form a straight line add to 180 degrees. The angles are supplementary.

Question 9

The measure of an angle is x degrees. Its complement measures 2x degrees. Find the value of x and the measure of each angle.

Accepted Answer

Since the angles are complementary, x + 2x = 90. This gives 3x = 90, so x = 30. The angles measure 30 degrees and 60 degrees.

Question 10

The measure of an angle is x degrees. Its supplement measures x + 40 degrees. Find the value of x and the measure of each angle.

Accepted Answer

Since the angles are supplementary, x + x + 40 = 180. This gives 2x + 40 = 180, so 2x = 140 and x = 70. The angles measure 70 degrees and 110 degrees.

Question 11

Decide whether angles measuring 38 degrees and 52 degrees are complementary, supplementary, or neither. Explain your answer.

Accepted Answer

The angles are complementary because 38 + 52 = 90, and complementary angles have a sum of 90 degrees.

Question 12

Decide whether angles measuring 95 degrees and 85 degrees are complementary, supplementary, or neither. Explain your answer.

Accepted Answer

The angles are supplementary because 95 + 85 = 180, and supplementary angles have a sum of 180 degrees.

Angle Relationships: Complementary and Supplementary

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