Question

6 fill in the blank 1 point find ( m angle c x y ). ( m angle c x y= ) type your answer...

Explanation:

Step1: Use the Side - Side - Side (SSS) Congruence

Since \(CX = XY\), \(CY=CY\), \(DY = EX\) (marked as equal in the figure), \(\triangle CEX\cong\triangle CDY\) (SSS congruence). So, \(\angle E=\angle D = 48^{\circ}\)

Step2: Use the Exterior Angle Theorem

In \(\triangle EXY\), \(\angle CXY\) is an exterior angle. By the exterior - angle theorem, \(\angle CXY=\angle E+\angle XYE\)

Since \(EX = XY\), \(\angle E=\angle XYE = 48^{\circ}\)

So, \(\angle CXY=48^{\circ}+ 89^{\circ}\)

Answer:

\(137^{\circ}\)