Questions: The triangle below has been extended to form an exterior angle of 163°. Find the value

The triangle below has been extended to form an exterior angle of 163°. Find the value
Transcript text: The triangle below has been extended to form an exterior angle of $163^{\circ}$. Find the value
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Solution

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Solution Steps

Step 1: Find the adjacent interior angle

The exterior angle of 163° and its adjacent interior angle form a linear pair, so they are supplementary and add up to 180°. Therefore, the adjacent interior angle is 180° - 163° = 17°.

Step 2: Find the value of x

The sum of the angles in a triangle is 180°. The two known angles are 17° and 115°. Therefore, x = 180° - 17° - 115° = 48°.

Final Answer

The value of x is 48°.

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