Angles Worksheets - Free Printable

Let’s solve each triangle problem one by one. We’ll use the fact that the exterior angle of a triangle equals the sum of the two opposite interior angles. Also, remember: angles on a straight line add up to 180°, and the three interior angles of any triangle add up to 180°.

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Problem 1:
Triangle with interior angles 46° and 59°, find exterior angle ∠GHI (at vertex H).
→ Exterior angle = sum of two opposite interior angles = 46° + 59° = 105°

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Problem 2:
Triangle with interior angles 72° and 32°, find exterior angle ∠HJK (at vertex J).
→ Exterior angle = 72° + 32° = 104°

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Problem 3:
Triangle with interior angles 41° and 37°, find exterior angle ∠KFG (at vertex F).
→ Exterior angle = 41° + 37° = 78°

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Problem 4:
Triangle with interior angles 44° and 29°, find exterior angle ∠JKL (at vertex K).
→ Exterior angle = 44° + 29° = 73°

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Problem 5:
Triangle with interior angles 37° and 57°, find exterior angle ∠KCH (at vertex C).
Wait — let’s check the diagram logic. If 37° and 57° are the two remote interior angles, then exterior angle = 37° + 57° = 94°

But wait — in some diagrams, the given angles might not both be interior. Let me double-check based on standard layout.

Actually, looking at typical problems like this: if you see two angles inside the triangle near the base, and you’re finding the exterior angle at the top or side, it’s usually the sum of the two non-adjacent interior angles.

Assuming that’s the case here too:

∠KCH is exterior → so it should equal sum of the two opposite interior angles: 37° + 57° = 94°

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Problem 6:
Triangle with interior angles 52° and 61°, find exterior angle ∠WVX (at vertex V).
→ Exterior angle = 52° + 61° = 113°

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Problem 7:
Triangle with interior angles 32° and 43°, find exterior angle ∠JGH (at vertex G).
→ Exterior angle = 32° + 43° = 75°

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Problem 8:
Isosceles triangle? Two angles marked as x, and one angle is 40°. Find exterior angle ∠LMN (at vertex M).

First, find the missing interior angle at M.

Sum of interior angles = 180°
So, x + x + 40° = 180°
→ 2x = 140° → x = 70°

Now, exterior angle at M = sum of the other two interior angles = 70° + 70° = 140°

Alternatively, since interior angle at M is 40°, exterior angle = 180° - 40° = 140° — same answer.

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Problem 9:
Triangle with interior angles 42° and 38°, find exterior angle ∠TUV (at vertex U).
→ Exterior angle = 42° + 38° = 80°

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✔ All answers checked using exterior angle theorem or straight-line rule.

Final Answer:
1) 105°
2) 104°
3) 78°
4) 73°
5) 94°
6) 113°
7) 75°
8) 140°
9) 80°