Virginia SOL Math / Grade 8 / Measurement & Geometry

8.MG.1

Angle-Pair Relationships

What you'll learn

  • Use angle-pair relationships to find unknown angle measures
  • Identify complementary, supplementary, vertical, and adjacent angles
  • Write and solve equations for unknown angles

Words to know

Complementary angles —
two angles whose measures add to 90 degrees
Supplementary angles —
two angles whose measures add to 180 degrees
Vertical angles —
opposite angles formed by two crossing lines; they are equal
Adjacent angles —
two angles that share a side and a vertex
Straight angle —
an angle that measures 180 degrees

Why it matters Angle relationships let us find missing measures in maps, designs, and structures without measuring every angle.

Worked examples

Model ItI do

Two angles are complementary. One measures 35 degrees. Find the other.

Complementary angles add to 90 degrees. Subtract: 90 - 35 = 55. The other angle measures 55 degrees.

Try It TogetherWe do

Angle A and angle B are supplementary. Angle A is 118 degrees. Find angle B.

Supplementary angles add to 180 degrees. Subtract: 180 - 118 = 62. Angle B measures 62 degrees.

Now YouYou do

Two lines cross. One of the four angles is 70 degrees. Find the measure of its vertical angle.

Recall that vertical angles are equal. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Two angles are complementary. One is 40 degrees. Find the other.

  2. 2.Two angles are supplementary. One is 100 degrees. Find the other.

  3. 3.Two lines cross. One angle is 45 degrees. What is its vertical angle?

On Level

The core Quick Check from the book.

  1. 1.Two angles are complementary. One is 62 degrees. Find the other.

  2. 2.Two angles are supplementary. One is 90 degrees. Find the other.

  3. 3.Vertical angles measure (2x) and 50 degrees. Find x.

  4. 4.An angle and its supplement are equal. What is each measure?

  5. 5.Angles measuring 3x and 2x are complementary. Find x.

Challenge

Stretch your thinking.

  1. 1.Two supplementary angles measure (3x + 10) and (2x) degrees. Find x.

  2. 2.An angle is 20 degrees more than its complement. Find the two angle measures.

  3. 3.Two lines cross. One of the four angles measures (4x) degrees and the angle adjacent to it measures (5x) degrees. Find x.