A triangle has three interior angles, and the sum of these angles is always \(180^\circ\).
This important rule helps us find any missing angle in a triangle when two angles are known.
In this lesson, we will use this rule to calculate the missing angle in different types of triangle problems.
Rule
The sum of the interior angles of a triangle is:
$$A + B + C = 180^\circ$$
To find a missing angle, subtract the known angles from \(180^\circ\).
Example
Find the missing angle \(x\) in the triangle:
\(A = 60^\circ\)
\(B = x\)
\(C = 30^\circ\)
$$60^\circ + x + 30^\circ = 180^\circ$$
$$90^\circ + x = 180^\circ$$
$$x = 90^\circ$$
So the missing angle is \(90^\circ\).
Video Explanation
Practice
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- Sum of Angles of a Triangle is 180° (Proof)
- Find the Missing Angle of a Triangle (Current lesson)