Question

a side of the triangle below has been extended to form an exterior angle of 149°. find the value of x.

Explanation:

Step1: Recall exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In a right - triangle, one of the non - adjacent interior angles to the given exterior angle is $90^{\circ}$ and the other is $x$. So, $149^{\circ}=x + 90^{\circ}$.

Step2: Solve for $x$

Subtract $90^{\circ}$ from both sides of the equation $149^{\circ}=x + 90^{\circ}$. We get $x=149^{\circ}-90^{\circ}$.

Answer:

$x = 59^{\circ}$