Question

an artist painting from a photo begins with a geometric sketch to match angle measures. what is the value of z?

z = □
(type a whole number)

Explanation:

Step1: Use the property of exterior angles

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 the triangle, if we assume the triangle has angles \(z\), \(17^{\circ}\), and the non - adjacent interior angle related to the \(105^{\circ}\) exterior angle. So, \(z + 17^{\circ}=105^{\circ}\).

Step2: Solve for \(z\)

Subtract \(17^{\circ}\) from both sides of the equation \(z + 17^{\circ}=105^{\circ}\). We get \(z=105 - 17\).

Answer:

\(z = 88\)