Question

1. find x, y, and z:

Explanation:

Step1: Find \( y \) using exterior angle property

In \(\triangle BCD\), \(y\) is the exterior angle. So, \(y = x + 27\). Also, since \(AC = AD = 10\), \(\triangle ACD\) is isosceles. And \(CD = BD = 10\), \(\triangle BCD\) is isosceles. So \(x = 27\) (base angles of isosceles \(\triangle BCD\)). Then \(y=x + 27=27+27 = 54\).

Step2: Find \( z \) using isosceles triangle property

Since \(AC = AD\), in \(\triangle ACD\), \(z=y = 54\) (base angles of isosceles triangle).

Answer:

\(x = 27\), \(y = 54\), \(z = 54\)