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Identify and Use Angle Relationships

Students identify and apply relationships among supplementary angles (sum to 180°), complementary angles (sum to 90°), vertical angles (equal), and adjacent angles. They write and solve equations to find unknown angle measures in geometric figures.

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Identify and Use Angle Relationships

Grade 7 · Geometry · question 1 of 3

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Two fences meet at a right angle at the corner of a garden, and a straight path leaves the corner between them. How many degrees is the angle marked with a question mark?

Find the angle marked ?.

How it is taught

0:00 of 4:44

Complementary angles add to 90 degrees.

The other angle is 90 minus the given angle.

Read it: Angle relationships

A right angle is split into two parts, and one part is 38°. The square mark means the whole is 90°, so the other part is 90 − 38 = 52°.

  1. Find the whole: a square mark is 90°, a straight line is 180°.
  2. Subtract the part you know from the whole.
  3. Where two lines cross, the opposite angles are equal.

Two angles that make a right angle add to 90°: they are complementary.

Two angles that make a straight line add to 180°: they are supplementary, like 38° and 180 − 38 = 142°.

Where two lines cross, the opposite angles are vertical angles. Each makes a straight line with the angle between them, so both are 180° less that angle: equal.

Complementary angles add to 90°, supplementary angles add to 180°, and vertical angles are equal.

Subtracting from 180 for a right angle: 180 − 38 = 142.

The square mark means 90°: 90 − 38 = 52.

Two angles are complementary. One is 41°. How many degrees is the other? — 49. Complementary angles add to 90°: 90 − 41 = 49.

Find x when 125° and x° sit on a straight line

Two angles meet along a straight line. One measures one hundred twenty-five degrees. What does the other one measure?

Here's the picture: a straight line, with a ray splitting it into two angles.

The angle on the left measures one hundred twenty-five degrees.

We'll call the angle on the right x degrees — that's the one we need to find.

Grade 7 · Using supplementary angles to find an unknown

Two angles that share a side and sit on a straight line are called supplementary. Together they always make one hundred eighty degrees.

So we can write an equation: one hundred twenty-five plus x equals one hundred eighty.

To get x by itself, subtract one hundred twenty-five from both sides.

One hundred eighty minus one hundred twenty-five is fifty-five.

So x equals fifty-five degrees. The two angles fit together to make a straight line — exactly one hundred eighty degrees!

Now you try. Find the missing angle on this drawing. What is the missing angle?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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