Let’s solve each triangle problem step by step.
Remember:
✔ The sum of all angles inside a triangle is always
180°.
✔ If an angle is outside the triangle (like in problems 4, 5, 8, 9, 12), it’s called an
exterior angle, and it equals the sum of the two opposite interior angles. Also, an exterior angle and its adjacent interior angle add up to
180°.
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Problem 1:
Angles: 70°, 45°, x°
→ 70 + 45 + x = 180
→ 115 + x = 180
→ x = 180 - 115 =
65
Problem 2:
Angles: 82°, 35°, x°
→ 82 + 35 + x = 180
→ 117 + x = 180
→ x = 180 - 117 =
63
Problem 3:
Angles: 58°, 86°, x°
→ 58 + 86 + x = 180
→ 144 + x = 180
→ x = 180 - 144 =
36
Problem 4:
This one has an exterior angle labeled x° next to a 61° angle.
The interior angles are 61° and 52°.
Exterior angle = sum of opposite interior angles → x = 61 + 52 =
113
*(Alternatively, find the third interior angle first: 180 - 61 - 52 = 67°, then x = 180 - 67 = 113° — same answer!)*
Problem 5:
We have a triangle with angles x°, y°, and 50°. Also, there’s an exterior angle of 120° next to y°.
Since exterior angle + adjacent interior = 180° → y = 180 - 120 =
60
Now, x + y + 50 = 180 → x + 60 + 50 = 180 → x = 180 - 110 =
70
Problem 6:
Angles: x°, 77°, 64°
→ x + 77 + 64 = 180
→ x + 141 = 180
→ x = 180 - 141 =
39
Problem 7:
Angles: x°, 13°, 29°
→ x + 13 + 29 = 180
→ x + 42 = 180
→ x = 180 - 42 =
138
Problem 8:
Triangle has angles 64°, 38°, q°. Exterior angle x° is next to q°.
First, find q: 64 + 38 + q = 180 → 102 + q = 180 → q = 78
Then, x = 180 - q = 180 - 78 =
102
*(Or use exterior angle rule: x = 64 + 38 = 102 — same!)*
Problem 9:
Angles: 81°, 69°, y° → first find y
81 + 69 + y = 180 → 150 + y = 180 → y =
30
Also, x° is exterior angle next to 69° → x = 180 - 69 =
111
*(Or x = 81 + 30 = 111 — same!)*
Problem 10:
Right triangle: 90°, 45°, x°
→ 90 + 45 + x = 180 → 135 + x = 180 → x =
45
Problem 11:
Angles: 35°, 15°, x°
→ 35 + 15 + x = 180 → 50 + x = 180 → x =
130
Problem 12:
Right triangle: 90°, 45°, x°
→ 90 + 45 + x = 180 → 135 + x = 180 → x =
45
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Final Answer:
1: 65
2: 63
3: 36
4: 113
5: x=70, y=60
6: 39
7: 138
8: x=102, q=78
9: x=111, y=30
10: 45
11: 130
12: 45
Parent Tip: Review the logic above to help your child master the concept of triangle worksheets.
