Question

In the given figure, if $AB=AC,CH=CB$ and $HK||BC$, then value of $\angle HCK$ is:

• A. ${30}^{\circ }$
• B. ${35}^{\circ }$
• C. ${40}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

Given exterior $\angle A$ = 140
Hence, $\angle BAC=180-140=40$
Since, $AB=AC$, $\angle ABC=\angle ACB$
In triangle $ABC$, $\angle ABC=\frac{180-40}{2}$ $=70$
Since, $HK\parallel BC$,
$\angle AHK=\angle AKH=\angle ABC=70$
$\angle AKH+\angle HKC=180$
$\angle HKC=110$
Since, $CH=CB$
$\angle BHC=\angle ABC=70$
$\angle BHC+\angle AHK+\angle CHK=180$
$\angle CHK=180-140=40$
Now, in triangle $CHK$
$\angle CHK+\angle HKC+\angle HCK=180$
$\angle HCK=180-150=30$.