Lesson 1Relationships of Angles

Learning Goal

Let’s examine some special angles.

Learning Targets

  • I can find unknown angle measures by reasoning about adjacent angles with known measures.

  • I can recognize when an angle measures , , or .

Lesson Terms

  • adjacent angles
  • right angle
  • straight angle

Warm Up: Visualizing Angles

Problem 1

  1. Which angle is bigger?

    Two angles a and b. The lines are shorter in a.

  2. Identify an obtuse angle in the diagram.

    Three lines intersecting at A with end points B, C, D. Angle DAC is 60 degrees and angle CAB is 50 degrees.

Activity 1: Pattern Block Angles

Problem 1

open applet in presentation mode

  1. Look at the different pattern blocks inside the applet. Each block contains either 1 or 2 angles with different degree measures. Which blocks have only 1 unique angle? Which have 2?

  2. If you place three copies of the hexagon together so that one vertex from each hexagon touches the same point, as shown, they fit together without any gaps or overlaps. Use this to figure out the degree measure of the angle inside the hexagon pattern block.

    3 hexagons pattern blocks drawn so that one vertex from each hexagon touches the same point and a circle is drawn around that point and "?" degrees are labeled on each hexagon

  3. Figure out the degree measure of all of the other angles inside the pattern blocks. (Hint: turn on the grid to help align the pieces.)

Print Version

  1. Trace one copy of every different pattern block. Each block contains either 1 or 2 angles with different degree measures. Which blocks have only 1 unique angle? Which have 2?

  2. If you trace three copies of the hexagon so that one vertex from each hexagon touches the same point, as shown, they fit together without any gaps or overlaps. Use this to figure out the degree measure of the angle inside the hexagon pattern block.

    3 hexagons pattern blocks drawn so that one vertex from each hexagon touches the same point and a circle is drawn around that point and "?" degrees are labeled on each hexagon

  3. Figure out the degree measure of all of the other angles inside the pattern blocks that you traced in the first question. Be prepared to explain your reasoning.

Are you ready for more?

Problem 1

We saw that it is possible to fit three copies of a regular hexagon snugly around a point.

Each interior angle of a regular pentagon measures . Is it possible to fit copies of a regular pentagon snugly around a point? If yes, how many copies does it take? If not, why not?

A hexagon with an interior angle of 108 degrees.

Activity 2: More Pattern Block Angles

Problem 1

Use pattern blocks to determine the measure of each of these angles.

  1. Two lines joined together to form angle a.
  2. Two lines joined together to form exterior angle b.
  3. A straight line with a point in the middle labeled angle C

Problem 2

If an angle has a measure of then the two legs form a straight line. An angle that forms a straight line is called a straight angle. Find as many different combinations of pattern blocks as you can that make a straight angle.

Use the applet if you choose. (Hint: turn on the grid to help align the pieces.) 

open applet in presentation mode
Print Version

If an angle has a measure of , then its sides form a straight line. An angle that forms a straight line is called a straight angle. Find as many different combinations of pattern blocks as you can that make a straight angle.

Activity 3: Measuring Like This or That

Problem 1

Tyler and Priya were both measuring angle .

A protractor with line S going through 40 degrees and line T going through 0

Priya thinks the angle measures 40 degrees. Tyler thinks the angle measures 140 degrees. Do you agree with either of them? Explain your reasoning.

Lesson Summary

When two lines intersect and form four equal angles, we call each one a right angle. A right angle measures . You can think of a right angle as a quarter turn in one direction or the other.

Two lines intersect to form an x shape. Where the lines intersect, a box is drawn around them and are all labeled 90 degrees.

An angle in which the two sides form a straight line is called a straight angle. A straight angle measures . A straight angle can be made by putting right angles together. You can think of a straight angle as a half turn, so that you are facing in the opposite direction after you are done.

A straight line with a center point and angle 180 degrees.

If you put two straight angles together, you get an angle that is . You can think of this angle as turning all the way around so that you are facing the same direction as when you started the turn.

A diagonal line with a circle around the end labeled 360 degrees.

When two angles share a side and a vertex, and they don’t overlap, we call them adjacent angles.