Question

what are the values of z and a?

z=

a=

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, \(z + 50^{\circ}=z+(z - 49^{\circ})\)

Step2: Solve the equation for \(z\)

$$
LATEXBLOCK0
$$

Step3: Find the value of \(a\)

Since \(a+(z + 50^{\circ})=180^{\circ}\) (linear - pair of angles), substitute \(z = 99^{\circ}\)

$$
LATEXBLOCK1
$$

Answer:

\(z = 99\), \(a = 31\)