Angles in a Triangle Worksheets - Math Monks - Free Printable

Let’s solve each triangle problem one by one, using the Triangle Angle Sum Theorem (sum of interior angles in any triangle = 180°) and properties of isosceles triangles (two equal sides → two equal base angles), and exterior angles when needed.

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Problem 1

Triangle ABC with:
- ∠A = 90° (right angle)
- ∠B = 49°
- Find ∠C (i.e., ∠ACB)

Solution:
Sum of angles = 180°
∠C = 180° - 90° - 49° = 41°

✔ Answer: ∠ACB = 41°

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Problem 2

Triangle ABC with:
- ∠B = 58°
- ∠C = 39°
- Find ∠A (∠BAC)

Solution:
∠A = 180° - 58° - 39° = 83°

✔ Answer: ∠BAC = 83°

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Problem 3

Triangle ABC with:
- ∠A = 38°
- ∠C = 90° (right angle)
- Find ∠B (∠ABC)

Solution:
∠B = 180° - 90° - 38° = 52°

✔ Answer: ∠ABC = 52°

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Problem 4

Triangle ABC with:
- ∠B = 77°
- Sides AB and BC are marked equal → isosceles triangle with AB = BC → base angles at A and C are equal.

So, ∠A = ∠C

Let ∠A = ∠C = x

Then:
x + x + 77° = 180°
2x = 103°
x = 51.5°

✔ Answer: ∠ACB = 51.5°

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Problem 5

Triangle ABC with:
- ∠A = 15°
- ∠C = 35°
- Find ∠B (∠ABC)

Solution:
∠B = 180° - 15° - 35° = 130°

✔ Answer: ∠ABC = 130°

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Problem 6

Triangle ABC with:
- ∠A = 120°
- Sides AB and AC are marked equal → isosceles triangle → base angles at B and C are equal.

So, ∠B = ∠C = x

Then:
120° + x + x = 180°
2x = 60°
x = 30°

✔ Answer: ∠ACB = 30°

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Problem 7

Triangle ABC with:
- ∠A = 100°
- Sides AB and AC are marked equal → isosceles triangle → base angles at B and C are equal.

So, ∠B = ∠C = x

Then:
100° + x + x = 180°
2x = 80°
x = 40°

✔ Answer: ∠ACB = 40°

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Problem 8

Triangle ABC with:
- ∠B = 30°
- ∠C = 35°
- Need to find ∠DAE, which is an exterior angle at vertex A.

First, find ∠BAC (interior angle at A):

∠BAC = 180° - 30° - 35° = 115°

Now, ∠DAE is the supplement of ∠BAC (they form a straight line at point A).

So:
∠DAE = 180° - 115° = 65°

✔ Answer: ∠DAE = 65°

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## ✔ Final Answers:

1. ∠ACB = 41°
2. ∠BAC = 83°
3. ∠ABC = 52°
4. ∠ACB = 51.5°
5. ∠ABC = 130°
6. ∠ACB = 30°
7. ∠ACB = 40°
8. ∠DAE = 65°

Let me know if you’d like diagrams or step-by-step visuals!