How to Find Interior Angles of Triangles
Concept
The angles that lie inside a shape, generally a polygon, are said to be interior angles.
In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle. A triangle with all three acute interior angles is called an acute triangle, a triangle with one interior angle as obtuse is known as an obtuse triangle, while a triangle with one interior angle as right angle is known as a right angled triangle.
Rules
The three angles of any triangle add up to 180 degrees.
To find any missing interior angle in a triangle, add the two angles given and then subtract from 180 degrees.
Example
What is the measure of the missing angle?
Solution
The three angles in a triangle add up to 180 degrees. We can find the missing angle by subtracting the two known angles from 180.
180° – 34° – 75°
= 71°
Practice How to Find Interior Angles of Triangles
Practice Problem 1
In the given triangle, find the value of x when given 2 angle measures.
Practice Problem 2
In the given triangle, find the value of x when given 2 angle measures.
Practice Problem 3
Find the value of the missing angles in the given situation by finding the value of x.
Interior angle – An angle that is one of the three angles inside of a triangle.
Exterior angle – An angle created by extending one side of a triangle beyond the vertex.
Related Skills
Geometric Proof
Polygons and Angles