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

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

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Solution Steps

Step 1: Identify the given angles

The triangle has three angles: 36°, 87°, and (6x + 3)°.

Step 2: Use the triangle angle sum property

The sum of the angles in a triangle is always 180°. Therefore, we can set up the equation: \[ 36° + 87° + (6x + 3)° = 180° \]

Step 3: Simplify the equation

Combine the constant terms on the left side of the equation: \[ 36 + 87 + 3 + 6x = 180 \] \[ 126 + 6x = 180 \]

Step 4: Solve for x

Subtract 126 from both sides of the equation: \[ 6x = 54 \] Divide both sides by 6: \[ x = 9 \]

Final Answer

\[ x = 9 \]

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Steve Hogan