Question

question
a side of the triangle below has been extended to form an exterior angle of 156°. find the value of x.
answer attempt 1 out of 2
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. Let the exterior angle be \(E = 156^{\circ}\), and the two non - adjacent interior angles be \(x\) and \(49^{\circ}\). So, \(E=x + 49^{\circ}\).

Step2: Solve for \(x\)

Rearrange the equation \(x=E - 49^{\circ}\). Substitute \(E = 156^{\circ}\) into the equation. Then \(x=156^{\circ}-49^{\circ}\).

$$x = 107^{\circ}$$

Answer:

\(x = 107\)