Question

Congruent sides are marked on the figure to the right. Find the values of x and y.

Answer 1

You can identify that the triangle ACD is divided into two different triangles. These triangles are ABD and BCD.

Notice that the triangle BCD has two congruent sides. Therefore, it is an Isosceles triangle.

The triangle ABD has three congruent sides. This means that it is an Equilateral triangle. The measure of each interior angle of and Equilateral triangle is:

`60\degree`

Therefore, you can determine that:

`x=60\degree`

Let's assume that ABD is a Right triangle. Then:

`ADC=90\degree`

Since the other triangle C has twol equal angles:

`m\angle BDC=y=90\degree-60\degree`

Therefore:

`y=30\degree`

The answer is:

`\begin{gathered} x=60\degree \\ y=30\degree \end{gathered}`