The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2.
29.6° , 49.7°

검증된 단계별 안내

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: the first angle is 29.6° and the second angle is 49.7°.

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

\[ 29.6 + 49.7 + x = 180 \]

Combine the known angles on the left side:

\[ 79.3 + x = 180 \]

Solve for \( x \) by subtracting 79.3 from both sides:

\[ x = 180 - 79.3 \]

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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 an unknown angle when the other two angles are known by subtracting their sum from 180°.

Basic Arithmetic Operations

Solving for the unknown angle requires simple arithmetic, specifically addition and subtraction. Adding the two given angles and subtracting their sum from 180° yields the measure of the third angle.

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 the given angle measures and performing calculations accurately.

The measures of two angles of a triangle are given. Find the measure of the third angle. See Example 2. 29.6° , 49.7°