Explore · MATH-5B-C11-L04-OPEN
A triangle has angles 49° and 72°. Find its third angle.
Singapore Math 5B · Original independent course
The Sum of the Angles in a Triangle
Watch for: Assuming all triangles contain a 90° angle.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C11-L04-PREREQ
Add the angles 60°, 60°, and 60°.
Show worked answer (after attempting)
Answer: 180°
60 + 60 + 60 = 180 degrees.
Understand the idea
Explain and use the 180° sum of interior triangle angles, including finding an unknown angle. The essential earlier idea is: Chapter 11 prior angle measurement and straight-line angle relationships.. The model below will always use the actual quantities from the worked problem. Check assuming all triangles contain a 90° angle when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C11-L04-Q01
A triangle has angles 48° and 72°. Find its third angle.
Solution: 60°
The interior angles make a straight angle: 48° + 72° + x = 180°. Therefore x = 180 − 48 − 72 = 60°.
Worked example 2 · MATH-5B-C11-L04-Q02
Two corners of a triangular badge are 68° and 51°. What is the remaining corner?
Solution: 61°
The interior angles make a straight angle: 68° + 51° + x = 180°. Therefore x = 180 − 68 − 51 = 61°.
Worked example 3 · MATH-5B-C11-L04-Q03
Explain why the third angle of a triangle with 39° and 86° cannot be 90°. Find it.
Solution: 55°
The interior angles make a straight angle: 39° + 86° + x = 180°. Therefore x = 180 − 39 − 86 = 55°.
Check understanding
1 · MATH-5B-C11-L04-Q04
A triangle has angles 49° and 72°. Find its third angle.
Show worked answer (after attempting)
Answer: 59°
The interior angles make a straight angle: 49° + 72° + x = 180°. Therefore x = 180 − 49 − 72 = 59°.
2 · MATH-5B-C11-L04-Q05
Two corners of a triangular badge are 69° and 51°. What is the remaining corner?
Show worked answer (after attempting)
Answer: 60°
The interior angles make a straight angle: 69° + 51° + x = 180°. Therefore x = 180 − 69 − 51 = 60°.
3 · MATH-5B-C11-L04-Q06
Explain why the third angle of a triangle with 40° and 86° cannot be 90°. Find it.
Show worked answer (after attempting)
Answer: 54°
The interior angles make a straight angle: 40° + 86° + x = 180°. Therefore x = 180 − 40 − 86 = 54°.
Guided practice
1 · MATH-5B-C11-L04-Q07
A triangle has angles 50° and 72°. Find its third angle.
Show worked answer (after attempting)
Answer: 58°
The interior angles make a straight angle: 50° + 72° + x = 180°. Therefore x = 180 − 50 − 72 = 58°.
2 · MATH-5B-C11-L04-Q08
Two corners of a triangular badge are 70° and 51°. What is the remaining corner?
Show worked answer (after attempting)
Answer: 59°
The interior angles make a straight angle: 70° + 51° + x = 180°. Therefore x = 180 − 70 − 51 = 59°.
3 · MATH-5B-C11-L04-Q09
Explain why the third angle of a triangle with 41° and 86° cannot be 90°. Find it.
Show worked answer (after attempting)
Answer: 53°
The interior angles make a straight angle: 41° + 86° + x = 180°. Therefore x = 180 − 41 − 86 = 53°.
4 · MATH-5B-C11-L04-Q10
A triangle has angles 51° and 72°. Find its third angle.
Show worked answer (after attempting)
Answer: 57°
The interior angles make a straight angle: 51° + 72° + x = 180°. Therefore x = 180 − 51 − 72 = 57°.
Independent practice
1 · MATH-5B-C11-L04-Q11
Two corners of a triangular badge are 71° and 51°. What is the remaining corner?
Show worked answer (after attempting)
Answer: 58°
The interior angles make a straight angle: 71° + 51° + x = 180°. Therefore x = 180 − 71 − 51 = 58°.
2 · MATH-5B-C11-L04-Q12
Explain why the third angle of a triangle with 42° and 86° cannot be 90°. Find it.
Show worked answer (after attempting)
Answer: 52°
The interior angles make a straight angle: 42° + 86° + x = 180°. Therefore x = 180 − 42 − 86 = 52°.
3 · MATH-5B-C11-L04-Q13
A triangle has angles 52° and 72°. Find its third angle.
Show worked answer (after attempting)
Answer: 56°
The interior angles make a straight angle: 52° + 72° + x = 180°. Therefore x = 180 − 52 − 72 = 56°.
4 · MATH-5B-C11-L04-Q14
Two corners of a triangular badge are 72° and 51°. What is the remaining corner?
Show worked answer (after attempting)
Answer: 57°
The interior angles make a straight angle: 72° + 51° + x = 180°. Therefore x = 180 − 72 − 51 = 57°.
5 · MATH-5B-C11-L04-Q15
Explain why the third angle of a triangle with 43° and 86° cannot be 90°. Find it.
Show worked answer (after attempting)
Answer: 51°
The interior angles make a straight angle: 43° + 86° + x = 180°. Therefore x = 180 − 43 − 86 = 51°.
6 · MATH-5B-C11-L04-Q16
A triangle has angles 53° and 72°. Find its third angle.
Show worked answer (after attempting)
Answer: 55°
The interior angles make a straight angle: 53° + 72° + x = 180°. Therefore x = 180 − 53 − 72 = 55°.
7 · MATH-5B-C11-L04-Q17
Two corners of a triangular badge are 73° and 51°. What is the remaining corner?
Show worked answer (after attempting)
Answer: 56°
The interior angles make a straight angle: 73° + 51° + x = 180°. Therefore x = 180 − 73 − 51 = 56°.
8 · MATH-5B-C11-L04-Q18
Explain why the third angle of a triangle with 44° and 86° cannot be 90°. Find it.
Show worked answer (after attempting)
Answer: 50°
The interior angles make a straight angle: 44° + 86° + x = 180°. Therefore x = 180 − 44 − 86 = 50°.
Challenge and error analysis
1 · MATH-5B-C11-L04-ERR1
The assigned question is: “Two corners of a triangular badge are 76° and 51°. What is the remaining corner?” A learner wrote: “I used 360 degrees as the triangle angle total instead of 180 degrees, so I wrote 53.1°.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 53°
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 53°. Recompute from the given data: The interior angles make a straight angle: 76° + 51° + x = 180°. Therefore x = 180 − 76 − 51 = 53°.
2 · MATH-5B-C11-L04-ERR2
The assigned question is: “Explain why the third angle of a triangle with 47° and 86° cannot be 90°. Find it.” A learner wrote: “I used 360 degrees as the triangle angle total instead of 180 degrees, so I wrote 48°.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 47°
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 47°. Recompute from the given data: The interior angles make a straight angle: 47° + 86° + x = 180°. Therefore x = 180 − 47 − 86 = 47°.
Exit check
Exit · MATH-5B-C11-L04-Q19
A triangle has angles 54° and 72°. Find its third angle.
Show worked answer (after attempting)
Answer: 54°
The interior angles make a straight angle: 54° + 72° + x = 180°. Therefore x = 180 − 54 − 72 = 54°.