Question

a side of the triangle below has been extended to form an exterior angle of 132°. find the value of x.
answer attempt 1 out of 2
x =

Explanation:

Step1: Find the adjacent interior angle

The adjacent interior angle to the \(132^{\circ}\) exterior angle is \(180 - 132=48^{\circ}\) (linear - pair angles sum to \(180^{\circ}\)).

Step2: Use the triangle - angle sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). Let the three interior angles of the triangle be \(x\), \(116^{\circ}\), and \(48^{\circ}\). Then \(x + 116+48 = 180\).
Simplify the left - hand side: \(x+164 = 180\).
Subtract \(164\) from both sides: \(x=180 - 164\).

Answer:

\(x = 16\)