Download A. Find the unknown angle measure in the

9-7 Angle Measures in Triangles
California
Standards
MG2.2 Use the properties of
complementary and supplementary
angles and the sum of the angles of a
triangle to solve problems involving an
unknown angle.
Also covered:
AF1.1, MG2.1
Holt CA Course 1
9-7 Angle Measures in Triangles
If you tear off the corners of a triangle and put all
three of them together, you will find that they
form a straight angle. This suggests that the sum
of the measures of the angles in a triangle is
180°.
Holt CA Course 1
9-7 Angle Measures in Triangles
Angles of a Triangle
The sum of the
measures of the
angles in a triangle
is 180°.
2
1
3
m1 + m2 + m3 = 180°
Holt CA Course 1
9-7 Angle Measures in Triangles
Additional Example 1: Finding an Angle Measure of
in a Triangle
A. Find the unknown angle
measure in each triangle.
80° + 55° + x = 180°
135° + x = 180°
–135°
–135°
55°
80°
The sum of the angle measures
in a triangle is 180°.
Add 55° and 80°.
Subtract 135° from both sides.
x = 45°
The measure of the unknown angle is 45°.
Holt CA Course 1
x
9-7 Angle Measures in Triangles
Additional Example 1: Finding an Angle Measure of
in a Triangle
x
B. Find the unknown angle
measure in each triangle.
34° + 90° + x = 180°
124° + x = 180°
–124°
–124°
34°
The sum of the angle measures
in a triangle is 180°.
Add 34° and 90°.
Subtract 124° from both sides.
x = 56°
The measure of the unknown angle is 56°.
Holt CA Course 1
9-7 Angle Measures in Triangles
Check It Out! Example 1
A. Find the unknown angle
measure in the triangle.
30°
x
90° + 30° + x = 180°
120° + x = 180°
–120°
–120°
The sum of the angle measures
in a triangle is 180°.
Add 30° and 90°.
Subtract 120° from both sides.
x = 60°
The measure of the unknown angle is 60°.
Holt CA Course 1
9-7 Angle Measures in Triangles
Check It Out! Example 1
B. Find the unknown angle
measure in each triangle.
22° + 90° + x = 180°
112° + x = 180°
–112°
–112°
x
22°
The sum of the angle measures
in a triangle is 180°.
Add 22° and 90°.
Subtract 112° from both sides.
x = 68°
The measure of the unknown angle is 68°.
Holt CA Course 1
9-7 Angle Measures in Triangles
Additional Example 2: Application
The figure shows part of
the support structure of a
bridge. Find the unknown
angle measure x. Show
D
your work.
A
75°
B
E
110°
x
C
Step 1: Find the measure of DEA.
mDEA + mDEC = 180°
mDEA + 110° = 180° Substitute 110° for mDEC.
mDEA = 70°
Holt CA Course 1
Subtract 110° from both
sides.
9-7 Angle Measures in Triangles
Additional Example 2 Continued
A
The figure shows part of
75° E
the support structure of a
110°
bridge. Find the unknown
x
angle measure x. Show
D
your work.
B
C
Step 2: Find the angle measure x.
70° + 75° + x = 180°
145° + x = 180°
x = 35°
Holt CA Course 1
Sum of angle measures
is 180°.
Add 70° and 75°.
Subtract 145° from both
sides.
9-7 Angle Measures in Triangles
Check It Out! Example 2
The figure shows a diagram A
E
of a design. Find the
95°
unknown angle measure x.
Show your work.
65°
D
B
x
C
Step 1: Find the measure of DEC.
mDEC + mDEA = 180°
mDEC + 95° = 180°
mDEC = 85°
Holt CA Course 1
Substitute 95° for mDEA.
Subtract 95° from both
sides.
9-7 Angle Measures in Triangles
Check It Out! Example 2 Continued
The figure shows a diagram
of a design. Find the
unknown angle measure x.
Show your work.
A
B
95°
D
E
65°
x
C
Step 2: Find the angle measure x.
Sum of angle measures is
85° + 65° + x = 180°
180°.
150° + x = 180°
x = 30°
Holt CA Course 1
Add 85° and 65°.
Subtract 150° from both
sides.