Lesson 13 Find Angle Measurements

    • Let’s compose and decompose angles to find their measurements.

Warm-up Notice and Wonder: Corner Pieces

What do you notice? What do you wonder?

Diagram with corners torn out and arranged into 90, 180, and 270 degree angles

Activity 1 How Big Are These Angles?

Problem 1

Your teacher will give you materials that can help you find angle measurements.
Use the materials and what you know about a right angle to find the size of angles , , , and . Be prepared to explain or show your reasoning.

  1. angle labeled p
  2. angle measured q
  3. angle labeled r
  4. angle labeled s

Problem 2

Next, use the measurements of angles , , , and to find the measurements of the following angles.

  1. obtuse angle with inside angle marked
  2. angle formed by two rays
  3. obtuse angle with outside marked
  4. angle with inside marked

Activity 2 Angles in a Kite

Your teacher will give you a square sheet of paper. Follow the steps to fold the paper into a kite. Fold as precisely as possible.

3 steps to fold a kite. 

Can you find the measurement of each labeled angle on the kite? If so, show your reasoning. If not, explain why not.

image of a kite. Top two angles labeled a, b. bottom two angles labeled c, d. Angles c and d together labeled e.

Practice Problems

Problem 1

  1. The circle is divided into 12 equal parts. What is the measure of angle ?

    Explain or show how you know.

    circle partitioned into 12 equal parts. 1 part labeled h.

  2. Can you put together angles to make a circle? How many of them will it take?

Problem 2

  1. A circle has been cut into eighths. How many degrees is the angle labeled ? Explain or show your reasoning.

    a circle cut in eigths with one angle labeled m

  2. Another circle has been cut into fifths. How many degrees is the angle labeled ? Explain or show your reasoning.

    a circle cut in fifths with one angle labeled p

Problem 3

  1. What is the measure of each angle ? Explain or show how you know.

    1 right angle partitioned into 4 smaller angles. One angle labeled, 15 degrees. 3 angles labeled p.

  2. How many angles can you fit together at one vertex without gaps or overlaps?