How do you use vertical and adjacent angles to find unknown angle measures?

For exampleWhat is the measure of angle x?

xo

115o

In this lesson you will learn to solve for unknown angle

measures by using vertical and adjacent angles.

Let’s ReviewLet’s Review

A straight angle measures exactly 180o.

180o

Let’s ReviewLet’s Review

Supplementary angles are two angles whose sum is 180o.

150o + 30o =180o

150o 30o

Let’s ReviewCore Lesson

A and B Streets intersect at an angle, as shown below. The city wants to add gardens in the areas formed by the intersection. The

designer needs to know the angles that the streets intersect in order to complete the designs. If it is known that one angle

measures 85o, what are the measures of the other three angles?

85o

xy

zA St. B St.

Let’s ReviewCore Lesson

x

y

z

85oAdjacent angles share a vertex

and a side. In this case, they are supplementary angles because

they are created by two intersecting lines.

85o + x = 180o

x = 95o

A St. B St.

Let’s ReviewCore Lesson

x

y

z

85o

y= 85o

z = 95o

A St. B St.

Vertical angles share a vertex but not a side. They have the same

measure.

In this lesson you have learned to solve for an unknown angle measure by using vertical and

adjacent angles.

Let’s ReviewGuided Practice

Find the unknown angle measures in the figure below.

55o

a b

c

Let’s ReviewExtension Activities

Find the unknown angle measures in the figure below.

39o 42o

Let’s ReviewExtension Activities

In the figure below Andrew stated that the measure of angle x is 72o. Is Andrew correct? Explain your reasoning.

72ox

yz

Let’s ReviewQuick Quiz

Use the figure below to determine the measures of angles a, b, and c.

Use the figure below to determine the measures of angles x, y, and z.

29oa

bc

71o xy

z