Geometry
Interior Angles of a Triangle
The three interior angles of any triangle always add up to 180°. Use this to find a missing angle when you know the other two.
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Worked Examples
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Problem
A triangle has angles 45° and 75°. Find the third angle.
Step-by-Step Solution
All three angles sum to 180°.
Third angle = 180° − 45° − 75° = 60°
Answer
60°
Problem
A right triangle has one angle of 35°. Find the other non-right angle.
Step-by-Step Solution
One angle = 90°, another = 35°.
Third angle = 180° − 90° − 35° = 55°
Answer
55°
Problem
An equilateral triangle has all equal angles. What is each angle?
Step-by-Step Solution
All three angles are equal and sum to 180°.
Each angle = 180° ÷ 3 = 60°
Answer
Each angle = 60°
Problem
A triangle has angles x, 2x, and 3x. Find each angle.
Step-by-Step Solution
All angles sum to 180°: x + 2x + 3x = 180°
6x = 180° → x = 30°
Angles are 30°, 60°, and 90°.
Answer
30°, 60°, 90°
Problem
Can a triangle have angles 95°, 50°, and 40°?
Step-by-Step Solution
Add the angles: 95 + 50 + 40 = 185°.
185° ≠ 180°.
No — the angles do not sum to 180°.
Answer
No — angles must sum to exactly 180°
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Angles are 50° and 80°. Find the third.
Angles are 90° and 42°. Find the third.
An isosceles triangle has a top angle of 40°. Find the base angles.
Angles are 60°, 60°, and x. Find x.
Angles are 110° and 35°. Find the third.
A triangle has angles 2x, 3x, and 4x. Find each angle.
Can a triangle have two right angles?
Angles are 25° and 130°. Find the third.
An isosceles triangle has base angles of 55°. Find the top angle.
A triangle has angles x and 2x and 90°. Find x.
Can a triangle have an angle of 0°?
Angles are 45°, 45°, and x. Find x.
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