Questions: A side of the triangle below has been extended to form an exterior angle of 128°. Find the value of x.

A side of the triangle below has been extended to form an exterior angle of 128°. Find the value of x.
Transcript text: A side of the triangle below has been extended to form an exterior angle of $128^{\circ}$. Find the value of $x$.
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Solution

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Solution Steps

Step 1: Find the adjacent interior angle

The exterior angle and its adjacent interior angle are supplementary, meaning they sum up to 180°. Therefore, the adjacent interior angle measures 180° - 128° = 52°.

Step 2: Use the triangle sum theorem

The sum of the interior angles of a triangle is always 180°. We know two of the angles are 106° and 52°. Thus, the third angle, _x_, is 180° - 106° - 52° = 22°.

Final Answer: The value of x is 22°

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