Questions: The measures of the angles of a triangle are shown in the fig below. Solve for x.

Transcript text: The measures of the angles of a triangle are shown in the fig below. Solve for x.

Solution

Step 1: Identify the given angles

The problem provides two angles of a triangle: 105° and 43°.

Step 2: Recall the sum of angles in a triangle

The sum of the interior angles in any triangle is always 180°.

Step 3: Set up the equation

Let \( x \) be the unknown angle. The equation based on the sum of the angles is: \[ x + 105° + 43° = 180° \]

Step 4: Solve for \( x \)

Combine the known angles: \[ 105° + 43° = 148° \] Subtract this sum from 180° to find \( x \): \[ x = 180° - 148° \] \[ x = 32° \]

\[ x = 32° \]

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