Calculating Angles in a Triangle
Using your knowledge of known facts about triangles, calculate the size of the missing angles
in the triangles below. Angles are not to scale.
1. 38°
2. 3.
72°
43°
20°
4. 5. 6.
32°
105°
64°
50°
7. 8. 9.
38°
40° 56° 20°
10. 11. 12.
23°
54°
120° 32°
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Calculating Angles in a Triangle
1. Ellie has measured the three angles in a triangle. One angle is 61° and another is 77°.
What is the measurement of the third angle?
2. Jake, Omar and Saskija are playing a game. Jake and Omar must give Saskija clues to help
her find the triangle that matches theirs.
Which triangle should Saskija choose? Angles are not to scale.
Jake:
The triangle has a right angle. 45°
Omar:
24°
It is a scalene triangle.
66°
45°
3. Dara is trying to solve a riddle. Her only clue is that the ratio of the three angles in the
mystery triangle is 2:3:4. Calculate the size of the angles and write them below from
smallest to largest:
4. Shaali, Caitlyn and Aleisha are investigating scalene triangles. They have each been given
a scalene triangle with one 52° angle labelled for them and two missing angles that they
must measure.
My missing angles My missing angles My missing angles
are 32° and 96°. are 27° and 120°. are 28° and 100°.
Shaali Caitlyn Aleisha
One of them has made a mistake. Who was it?
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Calculating Angles in a Triangle
5. Find the size of all of the angles in the triangle.
Angles are not to scale.
z
152°
° ° °
x= y= z=
6. Calculate the missing angles.
Angles are not to scale.
72°
56°
x
° ° °
x= y= z=
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Calculating Angles
in a Triangle Answers
1. 38°
2. 3.
72°
70°
71°
43°
71° 20° 65°
4. 5. 6.
80° 26°
43° 32°
105°
64°
50°
50°
7. 8. 9.
56°
122°
38°
50°
68°
40° 56° 20°
10. 11. 12.
58°
23°
63°
54°
63° 37°
120° 32°
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Calculating Angles in a Triangle Answers
1. Ellie has measured the three angles in a triangle. One angle is 61° and another is 77°.
What is the measurement of the third angle?
42°
2. Jake, Omar and Saskija are playing a game. Jake and Omar must give Saskija clues to help
her find the triangle that matches theirs.
Which triangle should Saskija choose?
Jake:
The triangle has a right angle. 45°
Omar:
24°
It is a scalene triangle.
66°
45°
3. Dara is trying to solve a riddle. Her only clue is that the ratio of the three angles in the
mystery triangle is 2:3:4. Calculate the size of the angles and write them below from
smallest to largest:
40° 60° 80°
4. Shaali, Caitlyn and Aleisha are investigating scalene triangles. They have each been given
a scalene triangle with one 52° angle labelled for them and two missing angles that they
must measure.
My missing angles My missing angles My missing angles
are 32° and 96°. are 27° and 120°. are 28° and 100°.
Shaali Caitlyn Aleisha
One of them has made a mistake. Who was it?
Caitlyn has made a mistake. (Her angles add up to more than 180°.)
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Calculating Angles in a Triangle Answers
5. Find the size of all of the angles in the triangle.
152°
28° 76° 76°
x= y= z=
6. Calculate the missing angles.
72°
56°
x
70° ° 54° ° 54° °
x= y= z=
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