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Geometry

Angle Pairs

Lesson

Four relationships between two angles come up over and over. Memorize them and most geometry computations are one subtraction away.

Complementary

Two angles whose measures sum to 90∘90^\circ.

∠A+∠B=90∘\angle A + \angle B = 90^\circ

Supplementary

Two angles whose measures sum to 180∘180^\circ.

∠A+∠B=180∘\angle A + \angle B = 180^\circ

Linear pair

Adjacent angles on a straight line. They are always supplementary.

Vertical angles

The opposite angles formed by two intersecting lines. They are always equal.

Worked example

The complement of 27∘27^\circ is 90−27=63∘90 - 27 = 63^\circ. The supplement is 180−27=153∘180 - 27 = 153^\circ.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Complement of 30∘\text{Complement of } 30^\circ

Problem 2

Supplement of 130∘\text{Supplement of } 130^\circ

Problem 3

Vertical angle to 70∘\text{Vertical angle to } 70^\circ

Problem 4

Linear pair partner of 110∘\text{Linear pair partner of } 110^\circ

Practice

Standard problems matching the lesson.

Problem 5

Complement of 45∘\text{Complement of } 45^\circ

Problem 6

Complement of 89∘\text{Complement of } 89^\circ

Problem 7

Complement of 10∘\text{Complement of } 10^\circ

Problem 8

Supplement of 45∘\text{Supplement of } 45^\circ

Problem 9

Supplement of 90∘\text{Supplement of } 90^\circ

Problem 10

Supplement of 1∘\text{Supplement of } 1^\circ

Problem 11

Vertical of 25∘\text{Vertical of } 25^\circ

Problem 12

Vertical of 144∘\text{Vertical of } 144^\circ

Problem 13

Linear pair partner of 60∘\text{Linear pair partner of } 60^\circ

Problem 14

Linear pair partner of 90∘\text{Linear pair partner of } 90^\circ

Problem 15

Complementary: one is 27∘. Other?\text{Complementary: one is } 27^\circ. \text{ Other?}

Problem 16

Supplementary: one is 33∘. Other?\text{Supplementary: one is } 33^\circ. \text{ Other?}

Problem 17

Vertical angles: 5x and 40. Find x.\text{Vertical angles: } 5x \text{ and } 40. \text{ Find } x.

Problem 18

Linear pair: 2x and 60. Find x.\text{Linear pair: } 2x \text{ and } 60. \text{ Find } x.

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Complement of 22.5∘\text{Complement of } 22.5^\circ

Problem 20

Linear pair: 7x and (3x+20). Find x.\text{Linear pair: } 7x \text{ and } (3x + 20). \text{ Find } x.

Problem 21

Vertical: 3x and 60. Find x.\text{Vertical: } 3x \text{ and } 60. \text{ Find } x.

Problem 22

An angle equals its complement. Each measures?\text{An angle equals its complement. Each measures?}

Problem 23

An angle is twice its supplement. Find the angle.\text{An angle is twice its supplement. Find the angle.}

Problem 24

Complementary: one is 3 times the other. Smaller?\text{Complementary: one is 3 times the other. Smaller?}

Problem 25

Linear pair in ratio 1:2. Smaller?\text{Linear pair in ratio 1:2. Smaller?}

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