Question

1. solve for x, y, and z.

x=
y=
z=

Explanation:

Step1: Find \(x\) using 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.
For the left - hand triangle, \(x=64 + 53\)

$$x=117$$

Step2: Find \(z\)

Since \(x\) and \(z\) are supplementary angles (\(x + z=180^{\circ}\))

$$z = 180 - x$$

Substitute \(x = 117\) into the equation: \(z=180 - 117\)

$$z = 63$$

Step3: Find \(y\)

For the right - hand triangle, using the angle - sum property of a triangle (\(34+z + y=180\))
Substitute \(z = 63\) into the equation: \(34+63 + y=180\)

$$y=180-(34 + 63)$$

$$y=180 - 97$$

$$y = 83$$

Answer:

\(x = 117\), \(y = 83\), \(z = 63\)