Question

question
a side of the triangle below has been extended to form an exterior angle of 157°. find the value of x.
157°
x°
103°
answer attempt 1 out of 2
x =
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Explanation:

Step1: Find the adjacent interior angle

Use the property that an exterior angle and its adjacent interior angle are supplementary (sum to \(180^{\circ}\)). Let the adjacent interior angle be \(y\). Then \(y + 157^{\circ}=180^{\circ}\), so \(y = 180^{\circ}- 157^{\circ}=23^{\circ}\).

Step2: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). In the triangle, we know two angles (\(y = 23^{\circ}\) and \(103^{\circ}\)), and let the third angle be \(x\). Then \(x+23^{\circ}+103^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(x+(23 + 103)^{\circ}=x + 126^{\circ}\).
So, \(x=180^{\circ}-126^{\circ}\).

Answer:

\(x = 54\)