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6-8 Grade 7 Unit 7 Lesson 3

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IM K-5 Math
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Lesson 3

3.1 Warm-up 3.2 Activity 3.3 Activity 3.4 Activity Student Lesson Summary Glossary

Unit 7, Lesson 3

Nonadjacent Angles

Grade 7

3.1

Warm-up

If is true, which statements also must be true?

and

3.2

Activity

Identify any pairs of angles in these figures that are complementary or supplementary.

A quadrilateral and a triangle. Please ask for futher assistance.

3.3

Activity

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 drawings and measurements created by others in your group. What patterns do you notice about the relationships between angle measures at an intersection?

3.4

Activity

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

column A

column B

is on Line . Find the value of .

A ray from point P, on line m, creates 2 angles, 134 degrees and a, degrees.

Find the value of .

A ray from the vertex of a right angle creates two angles, 44 degrees, b degrees.

Find the value of .

Two lines are perpendicular. A ray from the point where they meet creates 2 angles, 51 degrees, a, degrees.

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

A right triangle L M N. Angle N is 90 degrees, angle M is 51 degrees.

column A

column B

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

Quadrilateral C D E F. Angle C, 129 degrees.

is on line . Find the value of .

Point X is on line W Y. Rays V X and U X form 3 angles, b degrees, 95 degrees, 34 degrees.

Find the value of .

Three lines meet, forming 6 angles. The measures are, clockwise, c degrees, 42 degrees, 90 degress, d degrees, b degrees, 90 degrees.

is on line . Find the measure of angle .

Three lines meet, forming 6 angles. The measures are 67 degrees, 65 degrees, blank, blank, blank, blank.

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.

Student Lesson Summary

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

Two lines cross, with the 4 angles formed marked.

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

Two images. Both images intersecting lines, an obtuse angle, 150 degrees. One image, the angle adjacent counter-clockwise is 30 degrees, the other image, the angle adjacent clockwise is 30 degrees.

This is always true!

Two images. Both images intersecting lines, an obtuse angle, b. One image, the angle adjacent counter-clockwise is a, degrees, the other image, the angle adjacent clockwise is c degrees.

so .

so .

That means .

Vertical angles are opposite angles that share the same vertex. They are formed when two lines cross each other. Their angle measures are equal.

Angles and are vertical angles. If angle measures , then angle must also measure .

Angles and are another pair of vertical angles.

a pair of intersecting lines that create vertical angles.