The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 37° , 52°

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Recall that the sum of the interior angles of any triangle is always 180 degrees. This is a fundamental property of triangles.

Identify the given angles: 37° and 52°.

Set up an equation to find the third angle, which we'll call \( x \):

\[ 37 + 52 + x = 180 \]

Combine the known angles on the left side:

\[ 89 + x = 180 \]

Solve for \( x \) by subtracting 89 from both sides:

\[ x = 180 - 89 \]

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주요 개념

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Triangle Angle Sum Property

The sum of the interior angles of any triangle is always 180 degrees. This fundamental property allows us to find the measure of the third angle when the other two angles are known by subtracting their sum from 180°.

Basic Arithmetic Operations

To find the unknown angle, you need to perform simple addition and subtraction. First, add the two given angles, then subtract their sum from 180° to get the third angle's measure.

Angle Measurement Units

Angles are measured in degrees (°), a unit that divides a full rotation into 360 parts. Understanding this unit is essential for interpreting and calculating angle measures correctly.