Question

1. find the measures of x, y, and z. the triangle is not drawn to scale.

135° x°
z°

Explanation:

Step1: Find x (supplementary angles)

Supplementary angles sum to \(180^\circ\). So \(x + 135^\circ = 180^\circ\), thus \(x = 180 - 135 = 45^\circ\).

Step2: Identify triangle type (isosceles)

The triangle has two equal - marked sides, so it's isosceles. Thus, the base angles are equal, so \(z=x = 45^\circ\) (since the triangle is isosceles and the base angles are equal, and also using the supplementary angle property for \(z\) as we did for \(x\)).

Step3: Find y (triangle angle sum)

The sum of angles in a triangle is \(180^\circ\). So \(y+ x+z=180^\circ\). Substitute \(x = 45^\circ\) and \(z = 45^\circ\), we get \(y+45 + 45=180\), so \(y=180-(45 + 45)=90^\circ\).

Answer:

\(x = 45^\circ\), \(y = 90^\circ\), \(z = 45^\circ\)