Question

14 in the figure below, ( a b c d cong e f g h ). find ( x ) and ( y ).
( x=) and ( y=)

Explanation:

Step1: Find the value of \(x\)

Since \(ABCD\cong EFGH\), corresponding sides are equal. So, \(AD = EH\).
\(6x - 12=3x + 9\)
\(6x-3x=9 + 12\)
\(3x=21\)
\(x = 7\)

Step2: Find the value of \(y\)

Since \(ABCD\cong EFGH\), corresponding angles are equal. So, \(\angle C=\angle G\).
The sum of interior angles of a quadrilateral is \(360^{\circ}\). In quadrilateral \(ABCD\), \(\angle A = 90^{\circ},\angle B=81^{\circ},\angle C = 119^{\circ},\angle D=70^{\circ}\).
In quadrilateral \(EFGH\), \(\angle E = 90^{\circ}\).
Since \(\angle C=\angle G\), and using the angle - sum property of a quadrilateral \(360^{\circ}=\angle H+\angle E+\angle F+\angle G\).
We know that \(\angle G=\angle C = 119^{\circ}\), \(\angle E = 90^{\circ}\)
\(8y+39=119\)
\(8y=119 - 39\)
\(8y=80\)
\(y = 10\)

Answer:

\(x = 7\) and \(y = 10\)