Question

find the values of x and y.
x = 35 (simplify your answer.)
y = □ (simplify your answer.)

Explanation:

Step1: Use the property of isosceles triangle

Since \(AB = BC\), \(\angle A=\angle C = 35^{\circ}\), so \(x = 35\).

Step2: Use the property of right - angled triangle

In right - angled triangle \(ABD\), \(\angle ABD=90^{\circ}- 35^{\circ}=55^{\circ}\).
Since \(CD = BD\), \(\angle C=\angle CBD = 35^{\circ}\).
Then \(y=\angle ABD+\angle CBD=55^{\circ}+35^{\circ}=90^{\circ}\).

Answer:

\(x = 35\), \(y = 90\)