Question

a side of the triangle below has been extended to form an exterior angle of 125°. find the value of x.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In this right - angled triangle, the exterior angle \(125^{\circ}\) is equal to the sum of the right angle (\(90^{\circ}\)) and the angle \(x\). So, we can write the equation \(x + 90^{\circ}=125^{\circ}\).

Step2: Solve for \(x\)

Subtract \(90^{\circ}\) from both sides of the equation \(x + 90^{\circ}=125^{\circ}\).

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Answer:

\(x = 35\)