Lesson 3Nonadjacent Angles

Learning Goal

Let’s look at angles that are not right next to one another.

Learning Targets

  • I can determine if angles that are not adjacent are complementary or supplementary.

  • I can explain what vertical angles are in my own words.

Lesson Terms

  • adjacent angles
  • complementary
  • right angle
  • straight angle
  • supplementary
  • vertical angles

Warm Up: Finding Related Statements

Problem 1

Given and are numbers, and , which statements also must be true?

  4. and

Activity 1: Polygon Angles

Problem 1

Use any useful tools in the geometry toolkit to identify any pairs of angles in these figures that are complementary or supplementary.

A parallelogram ABCD and right triangle EFG.

Activity 2: Vertical Angles

Problem 1

Use a straightedge to draw two intersecting lines. Use a protractor to measure all four angles whose vertex is located at the intersection.

Compare your drawing and measurements to the people in your group. Make a conjecture about the relationships between angle measures at an intersection.

Activity 3: Row Game: Angles

Problem 1

Find the measure of the angles in one column. Your partner will work on the other column. Check in with your partner after you finish each problem part. Your answers in each part should be the same. If your answers aren’t the same, work together to find the error and correct it.

  1. column A

    column B

    is on line . Find the value of .

    Line m with a point P and a line extending at an angle with obtuse angle 134 and acute angle a.

    Find the value of .

    Two lines forming a right angle with a third line intersecting them with one angle 44 degrees and other angle b.

  2. column A

    column B

    Find the value of .

    Two lines making a right angle with a third line intersecting them with a 51 degree angle and angle a.

    In right triangle , angles and are complementary. Find the measure of angle .

    A right triangle with angle M , 51 degrees.

  3. column A

    column B

    Angle and angle are supplementary. Find the measure of angle .

    Trapezoid CDEF with 125 degree angle, C.

    is on line . Find the value of .

    Two lines V and U intersecting at point x on line YW. Angle VXY is b, angle VXW is 95 degrees and angle UXW is 34 degrees.

  4. column A

    column B

    Find the value of .

    Vertical, horizontal, and diagonal lines intersecting with angles labeled a, b, c, and 42.

    is on line . Find the measure of angle .

    A horizontal line FW intersected by two lines, DU and CE at point B. Angle DBC is 65 degrees. Angle DBF is 67 degrees.

  5. column A

    column B

    Two angles are complementary. One angle measures 37 degrees. Find the measure of the other angle.

    Two angles are supplementary. One angle measures 127 degrees. Find the measure of the other angle.

Lesson Summary

When two lines cross, they form two pairs of vertical angles. Vertical angles are across the intersection point from each other.

Two intersecting lines with a circle around the intersection

Vertical angles always have equal measure. We can see this because they are always supplementary with the same angle. For example:

Two intersecting lines with angle 30 degrees and 150 degrees

This is always true!

Two intersecting lines with angle a and b

so .

so .

That means .