Question

Using the information given in the figure, find the values of x and y.

• A. $x=7,y=8$
• B. $x=5,y=8$
• C. $x=7,y=6$
• D. $x=5,y=7$

Answer 1

The correct option is A

$x=7,y=8$

In $△ABD$ and $△CDB$

(i) $\angle BAD=\angle DCB$ ... (given)

(ii) $\angle ABD=\angle CDB$ ... (given)

(iii) BD = BD ... (common)

(iv) $△ABD\cong △CDB$ ... (AAS Postulate)

(v) AB = CD ... (cpct)

$5x-7=28$

$5x=35$

$x=7$

(vi) AD = BC ... (cpct)

$8y-18=46$

$8y=64$

$y=8$

Hence (A) is correct option