Question

triangle abc is shown with exterior \\( \angle z \\).

determine \\( m \angle z \\).

\\( 49 ^ { \circ } \\)
\\( 97 ^ { \circ } \\)
\\( 131 ^ { \circ } \\)
\\( 146 ^ { \circ } \\)

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 triangle \(ABC\), \(\angle z\) is an exterior angle. The two non - adjacent interior angles are \(97^{\circ}\) and \(34^{\circ}\).

Step2: Calculate \(m\angle z\)

$$m\angle z=97^{\circ}+34^{\circ}$$

$$m\angle z = 131^{\circ}$$

Answer:

\(131^{\circ}\)