Question

In the given figure, ABCD is a kite with AC and BD as diagonals and $\angle ABC$ = ${30}^{\circ }$. Find $x$.

• A. ${75}^{\circ }$
• B. ${85}^{\circ }$
• C. ${80}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is A

${75}^{\circ }$

From the figure, the diagonal AC divides the kite into two isoceles triangles.


In $△ABC$, $AB=CB$ (Adjacent sides of kite ABCD )

Given, $\angle ABC$ = 30°.
Since, $AB=BC,\angle BAC=\angle BCA$
Then, $\angle BCA=\angle BAC=x$

By, angle sum property of a triangle,
$\angle ABC+\angle BCA+\angle BAC$ = 180°
$\Rightarrow 30°+x+x=180°$
$\Rightarrow 30°+2x=180°$
$\Rightarrow 2x=180°-30°=150°$
$\Rightarrow x=75°$

Hence, the value of $x$ is $75°.$