Lesson 15 Reasoning About Angles (Part 2)

    • Let’s figure out missing angle measurements.

Warm-up How Many Do You See: Obtuse Angles

How many angles do you see in the folded paper heart?

photo of a paper folded heart

Activity 1 Shaded and Unshaded Angles

Find the measurement of each shaded angle. Show how you know.

  1. a right angle divided in two sections with one section labeled 62 degrees
  2. a straight angle divided in 3 sections with one marked as a right angle and another labeled 71 degrees
  3. a straight angle divided in 2 sections on top with one labeled 108 degrees and divided in 2 sections on bottom with one labeled 54 degrees
  4. vertical angles with one labeled 43 degrees

Activity 2 Info Gap: A Whole Bunch of Angles

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

image of information gap card

Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.

Practice Problems

Problem 1

Find the measure of each labeled angle in the drawing. Assume that:

  • The angles of the triangles meeting at the point in the middle of the figure are all the same.

  • The other angles of the triangles all have the same measure.

8 sided shape partitioned into 8 triangles of the same size.

Problem 2

In this diagram each angle on the left hand side is the same as the corresponding angle on the right hand side. Find the measure of angles , , and . Explain or show your reasoning.

diagram composed of shapes and angles.