2. Main Idea and New Vocabulary Key Concept: Angles of a Triangle
Example 1: Find Angle Measures
Example 2: Use Ratios to Find Angle Measures
Key Concept: Classify Triangles
Example 3: Classify Triangles
Example 4: Classify Triangles
Lesson Menu

3. Find missing angle measures in triangles.
acute triangle
right triangle
obtuse triangle
scalene triangle
isosceles triangle
equilateral triangle
Main Idea/Vocabulary

4. Key Concept

5. x + 36 + 36 = 180 Write the equation. x + 72 = 180 Simplify.
Find Angle Measures
PARK The city park shown is in the shape of a triangle. Find the value of x.
x = 180 Write the equation.
x + 72 = 180 Simplify.
– – 72 Subtract.
x = 108 Simplify.
Answer: The value of x is 108°.
Example 1

6. STONES The paver stone shown below is in the shape of a triangle
STONES The paver stone shown below is in the shape of a triangle. Find the value of x.
A. 39°
B. 56°
C. 73°
D. 146°
Example 1 CYP

7. Use Ratios to Find Angle Measures
The measures of the angles of ΔDEF are in the ratio 1:2:3. What are the measures of the angles?
Example 2

8. Use Ratios to Find Angle Measures
x + 2x + 3x = 180 Write the equation.
6x = 180 Combine like terms.
x = 30 Simplify.
Since x = 30, 2x = 2(30) or 60, and 3x = 3(30) or 90.
Answer: The measures of the angles are 30°, 60°, and 90°.
Example 2

9. The measures of the angles of ΔQRS are in the ratio 1:3:6
The measures of the angles of ΔQRS are in the ratio 1:3:6. What are the measures of the angles?
A. 18°, 36°, 54°
B. 18°, 54°, 108°
C. 15°, 45°, 90°
D. 30°, 60°, 90°
Example 2 CYP

10. Key Concept 3

11. Classify the triangle by its angles and by its sides.
Classify Triangles
Classify the triangle by its angles and by its sides.
The triangle has a right angle and no congruent sides.
Answer: It is a right scalene triangle.
Example 3

12. Classify the triangle by its angles and by its sides.
A. acute scalene
B. acute isosceles
C. obtuse scalene
D. obtuse isosceles
Example 3 CYP

13. Classify the triangle by its angles and by its sides.
Classify Triangles
Classify the triangle by its angles and by its sides.
The triangle has all acute angles and two congruent sides.
Answer: It is an acute isosceles triangle.
Example 4

14. Classify the triangle by its angles and by its sides.
A. acute scalene
B. acute isosceles
C. right scalene
D. right isosceles
Example 4 CYP