Triangle Sum Secrets Handout
Angle Relationships in Triangles
Student Handout
Name
Date
Pd
Angles
of a
Triangle
-
• Triangles can be named by the three angles. They can be described by terms , , and .
-
• Angles can be named in two different ways:
-
∠A: angle
or
-
∠B: angle
or
-
∠C: angle
or
A B C
-
• The of the three angles is .
Determine the missing angle in the triangles below.
1. Find the measure of ∠C.
B A C 32° 81°
Equation:
m∠C:
2. Find the measure of ∠F.
E D F 45°
Equation:
m∠F:
3. Find the measure of ∠HIG.
H G I 58° 51°
Equation:
m∠HIG:
4. Real World Application
A carpenter builds a support beam. Two angles measure 40° and 70°. Determine the third angle.
Equation:
Angle:
©Maneuvering the Middle LLC, 2016 (Modified)
Mark the statements in questions 5-7 as true or false. Then correct the false statement in the space provided.
L K M 35° 75°
a. The measure of ∠LKM is 35°, the measure of ∠KML is 75° and the measure of ∠KLM is unknown.
b. The equation 110 + x = 180 can be used to find the measure of ∠KLM.
c. The measure of ∠KLM is 35°.
Correct the false statement:
B A C 60° 60°
a. Both ∠B and ∠A are acute angles.
b. The equation 120 + x = 180 can be used to find the measure of ∠BCA.
c. The measure of ∠BCA is 60°.
Correct the false statement:
V W X 20° 40°
a. The equation 20 + x = 40 can be used to find the measure of ∠VWX.
b. The measure of ∠XWV is 120°.
c. Triangle VWX is an obtuse triangle.
Correct the false statement:
Use your understanding of triangles to answer the questions below.
8. The measure of angle G is 35° and the measure of angle E is 65°. Which of the following must be the measure of angle F in order to form triangle EFG?
A. 110°
B. 80°
C. 100°
D. 70°
9. Mrs. Tonell writes the measure of 3 angles on the board. Rachel says the three angles will form a triangle. Do you agree or disagree? Explain.
∠M = 50°
∠N = 80°
∠O = 60°
Summarize today's lesson:
Triangle Sum Secrets Answer Key
Angle Relationships in Triangles
Answer Key
Angles
of a
Triangle
- ...described by terms acute, right, and obtuse.
-
- ∠A: ∠CAB / ∠BAC
- ∠B: ∠ABC / ∠CBA
- ∠C: ∠BCA / ∠ACB
- The sum of the angles is 180°.
1. m∠C
Eq: 113 + x = 180
m∠C: 67°
2. m∠F
Eq: 135 + x = 180
m∠F: 45°
3. m∠HIG
Eq: 109 + x = 180
m∠HIG: 71°
4. Real World
Eq: 110 + x = 180
Angle: 70°
Answer Key Continued
5. a. True | b. True | c. False (Angle is 70°)
6. a. True | b. True | c. True
7. a. False (Eq: 60+x=180) | b. True | c. True
8. B (80°)
9. Disagree
(Sum = 190°)
Lesson Summary Answer:
Angles in a triangle always add up to 180. To find a missing angle, add the knowns and subtract the total from 180.
Triangle Sum Exit Ticket
Triangle Sum Exit Ticket
Name:
1. Find the measure of ∠C.
B A C 40° 80°
Equation:
m∠C:
2. Real World Scenario
A triangular garden path has two corners that measure 60° and 60°. What is the measure of the third corner?
Answer:
"The sum of all three interior angles in any triangle is always _______°."
Triangle Sum Exit Ticket
Name:
1. Find the measure of ∠C.
B A C 40° 80°
Equation:
m∠C:
2. Real World Scenario
A triangular garden path has two corners that measure 60° and 60°. What is the measure of the third corner?
Answer:
"The sum of all three interior angles in any triangle is always _______°."
Triangle Sum Practice Packet
Triangle Sum Practice
Independent Work
Name:
Date:
Directions: Find the missing angle measurement for each triangle below. Show your work by writing a 1-step equation.
1. Find the measure of ∠C.
B A C 32° 81° x
Equation:
m∠C:
2. Find the measure of ∠F.
E D F 50° x
Equation:
m∠F:
3. Road Signs
A standard Yield sign is a triangle. If two of the interior angles measure 60° each, what is the measure of the third angle?
Equation:
Answer:
4. Pizza Slice
A slice of pizza has angles measuring 30° and 75°. Find the measure of the third angle of the slice.
Equation:
Answer:
Part 2: Real World Triangles
5. Camping Equipment
The peak of an A-frame tent measures 80°. One of the bottom base angles measures 50°. Determine the measurement of the other base angle.
Equation:
Missing Angle:
6. Construction Tools
A specialized metal bracket is a right triangle. If one angle is 90° and another is 25°, find the third angle of the bracket.
Equation:
Missing Angle:
7. Recreational Kites
In a diamond-shaped kite made of two triangles, the top triangle has angles of 44° and 68°. Find the third angle measurement.
Equation:
Missing Angle:
Part 3: Advanced Structure
8. Bridge Truss Design
Engineers use triangular trusses to build strong bridges. Solve for angles A and B in the diagram below.
55° 70° A 45° B 45°
Solve for Angle A:
Solve for Angle B:
9. Structural Challenge
A specific roof truss design includes one 90° angle. If the other two angles are exactly the same size, what must be the measurement of each angle? Explain your logic.
Angle Measurement:
