Question

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

Explanation:

Step1: Use the property of congruent triangles (SAS)

Since \(AB = BC\) (given by the marks), \(AD = DC = 6\) (given by the marks), and \(\angle A=55^{\circ}\), and \(\triangle ABD\cong\triangle CBD\) (by Side - Angle - Side (SAS) congruence: \(AB = BC\), \(BD=BD\) (common side), \(AD = DC\)). Then \(\angle A=\angle C = 55^{\circ}\), and \(\angle ABD=\angle CBD=x\).

Step2: Use the angle - sum property of a triangle

In \(\triangle ABC\), \(\angle A+\angle ABC+\angle C=180^{\circ}\). Since \(\angle ABC = 2x\), we have \(55^{\circ}+2x + 55^{\circ}=180^{\circ}\).

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Answer:

\(x = 35\)