Question

Using the information given in the figure, the values of x and y are __

• A. $x=15,y={60}^{\circ }$
• B. $x=15,y={30}^{\circ }$
• C. $x=30,y={30}^{\circ }$
• D. $x=10,y={60}^{\circ }$

Answer 1

The correct option is B

$x=15,y={30}^{\circ }$

In $△BAD$ and $△CAD$

(i) AD = AD ......(common)

(ii) $\angle ADB=\angle ADC={90}^{\circ }$ .....(given)

(iii) BD = CD .....(given)

$△BAD\cong △CAD$..... (SAS postulate)

(iv) AB = AC ......(CPCT)

$3x-17=x+13$

$2x=30$

$\Rightarrow$ $x=15$

(vi) $\angle BAD=\angle CAD$ ........(cpct)

$\angle BAD={30}^{\circ }$ (sum of angles of $△ADB$)

$\therefore$ $y^{\circ }=\angle BAD={30}^{\circ }$