Angles in a Triangle Worksheets - Math Monks - Free Printable

I will solve this worksheet by finding the missing angle 'a' for each of the 8 triangles. The key principle I will use is that the sum of the interior angles in any triangle is always 180 degrees.

Let me go through each problem one by one:

Problem 1:
- Given angles: 70° and 35°
- Missing angle 'a': a = 180° - 70° - 35° = 75°

Problem 2:
- Given angles: 82° and 44°
- Missing angle 'a': a = 180° - 82° - 44° = 54°

Problem 3:
- Given angles: 117° and 17°
- Missing angle 'a': a = 180° - 117° - 17° = 46°

Problem 4:
- This is an isosceles triangle (indicated by the tick marks on two sides, meaning those sides are equal, and therefore the base angles are equal).
- One base angle is given as 68°, so the other base angle is also 68°.
- Missing angle 'a': a = 180° - 68° - 68° = 44°

Problem 5:
- This is also an isosceles triangle (tick marks on two sides).
- One angle is given as 42°, and since the tick marks are on the sides adjacent to the missing angle 'a', the two base angles are equal.
- So, the two base angles are both 42°.
- Missing angle 'a': a = 180° - 42° - 42° = 96°

Problem 6:
- This is an equilateral triangle (all three sides have tick marks, meaning all sides are equal, and therefore all angles are equal).
- All angles in an equilateral triangle are 60°.
- Missing angle 'a': a = 60°

Problem 7:
- This problem shows an exterior angle 'a'.
- The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
- The two opposite interior angles are 40° and 17°.
- Missing angle 'a': a = 40° + 17° = 57°

Problem 8:
- This problem also shows an exterior angle 'a'.
- The exterior angle is equal to the sum of the two opposite interior angles.
- The two opposite interior angles are 88° and 39°.
- Missing angle 'a': a = 88° + 39° = 127°

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Here are the final answers for each problem:
1. 75°
2. 54°
3. 46°
4. 44°
5. 96°
6. 60°
7. 57°
8. 127°