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The sum of angles in a triangle
Learn step-by-step with practice exercises built right in.
The sum of the interior angles of any triangle is .
Two angles of a triangle measure and . Find the third angle.
Use the Triangle Angle Sum Theorem:
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Explore more Geometry topics
Acute Triangle: All three angles are acute (< 90°)
Right Triangle: One angle is exactly 90°
Obtuse Triangle: One angle is obtuse (> 90°)
Equiangular Triangle: All three angles equal 60°
An exterior angle of a triangle equals the sum of the two remote interior angles.
Example: If an exterior angle measures , and one remote interior angle is , the other remote interior angle is:
The measure of each angle of an equilateral triangle is .
This theorem is used to:
Answer:
In a triangle, the angles are in the ratio . Find all three angle measures.
Let the angles be , , and .
The three angles are:
Check: ✓
Answer: , ,
An exterior angle of a triangle measures . One of the remote interior angles measures . Find the other two angles of the triangle.
Step 1: Use Exterior Angle Theorem
The exterior angle equals the sum of remote interior angles:
So one remote interior angle is .
Step 2: Find the third angle (adjacent to exterior)
The exterior angle and its adjacent interior angle are supplementary:
The three angles are: , ,
Check: ✓
Answer: The three angles are , , and