Question

In $△XYZ,\angle Z={90}^o$ and $xz=\frac{1}{2}xy$ then ____ is true from the following

• A. $m\angle Y={30}^o$
• B. $m\angle X={45}^o$
• C. $m\angle X={40}^o$
• D. $m\angle X={30}^o$

Answer 1

The correct option is A $m\angle Y={30}^o$

Since $xz=\frac{1}{2}xy$

$\sin y=\frac{xz}{xy}$

$\Rightarrow \sin y=\frac{\frac{1}{2}x\times y}{xy}$

$\Rightarrow \sin y=\frac{1}{2}$

$\Rightarrow y={30}^0$

$\angle x+\angle y+\angle z={180}^0$

$\Rightarrow \angle x+{30}^0+{90}^0={180}^0$

$\Rightarrow \angle x={90}^0-{30}^0$

$\Rightarrow \angle x={60}^0$