Question

a side of the triangle below has been extended to form an exterior angle of 143°. find the value of x.
answer attempt 1 out of 2
x =

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle and the exterior angle of \(143^{\circ}\) are supplementary. So the adjacent interior angle is \(180 - 143=37^{\circ}\).

Step2: Use the triangle angle - sum property

In a right - angled triangle, the sum of the two non - right angles is \(90^{\circ}\). Let the two non - right angles be \(37^{\circ}\) and \(x^{\circ}\). Then \(x + 37=90\).

Step3: Solve for \(x\)

Subtract \(37\) from both sides of the equation \(x + 37=90\). We get \(x=90 - 37\).

Answer:

\(x = 53\)