(8) Lesson 5.3 - Angles of Triangles

1. Course 3, Lesson 5-3
1. The statements for a two-column proof
to show that angle C = 47° are given below.
Complete the proof by providing the reasons.
2. Refer to the triangle shown at right.
What conclusion can you make about
the value of x?

2. Course 3, Lesson 5-3
ANSWERS
1. Given; Definition of triangle; Substitution;
Subtraction Property of Equality
2. x = 60

3. HOW can algebraic concepts be
applied to geometry?
Geometry
Course 3, Lesson 5-3

4. Course 3, Lesson 5-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices
and Council of Chief State School Officers. All rights reserved.
Geometry
• 8.G.5
Use informal arguments to establish facts about the angle sum and exterior
angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for similarity of triangles.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. To
• find missing angle measures in a triangle,
• find missing angle measures in a triangle
using the exterior angles
Course 3, Lesson 5-3
Geometry

6. • triangle
• interior angle
• exterior angle
• remote interior angles
Course 3, Lesson 5-3
Geometry

7. Course 3, Lesson 5-3
Geometry
Words The sum of the measures of the interior angles of a
triangle is 180˚
Model
Symbols x + y + z = 180˚

8. 1
Need Another Example?
2
Step-by-Step Example
1. Find the value of x in the
Antigua and Barbuda flag.
x + 55 + 90 = 180
The value of x is 35.
x + 145 = 180
– 145 = – 145
x = 35
Write the equation.
Simplify.
Subtract.
Simplify.

9. Answer
Need Another Example?
The city park shown at the
right is in the shape of a
triangle. Find the value of x.
116

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. The measures of the angles of ABC are in the
ratio 1:4:5. What are the measures of the angles?
Let x represent the measure of angle A.
Since x = 18, 4x = 4(18) or 72, and 5x = 5(18) or 90.
The measures of the angles are 18°, 72°, and 90°.
x + 4x + 5x = 180
x = 18
Write the equation.
Then 4x and 5x represent angle B and angle C.
10x = 180 Collect like terms.
Division Property of Equality

11. Answer
Need Another Example?
The measures of the angles of triangle DEF
are in the ratio 1:2:3. What are the measures
of the angles?
30°, 60°, and 90°

12. Course 3, Lesson 5-3
Geometry
Words The measure of an exterior angle of a triangle is equal to
the sum of the measures of its two remote interior angles.
Model
Symbol 1m A m B    

13. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. Suppose m∠4 = 135°.
Find the measure of ∠2.
Angle 4 is an exterior angle.
Its two remote interior angles
are ∠2 and ∠LKM.
So, the m∠2 = 45°.
x + 90° = 135°
x = 45°
Write the equation.m∠2 + m∠LKM = m∠4
m∠2 = x°, m∠LKM = 90°, m∠4 = 135°
Subtraction Property of Equality

14. Answer
Need Another Example?
Find the value of x in
the triangle.
80

15. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-3
Geometry

16. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-3
Geometry
Sample answer:
• Since the sum of the measures of any triangle is 180°,
you can write and solve an equation to find the missing
measure of an angle.

17. You are given the measures
of two interior angles of a
triangle. Describe the steps
you would take to find the
missing interior angle
measure of the triangle.
Ratios and Proportional RelationshipsFunctionsGeometry
Course 3, Lesson 5-3