Question

In figure, if $l\parallel m$, then the value of $x$ is:

• A. ${30}^o$
• B. ${45}^o$
• C. ${50}^o$
• D. ${60}^o$

Answer 1

The correct option is D ${60}^o$

Since $l\parallel m$, then
$3y=2y+{25}^0$ [Alternate $\angle s$]
$\Rightarrow 3y-2y={25}^0$
$\Rightarrow y={25}^0$ ......(1)
Also $x+{15}^0=2y+{25}^0$ [Vertically opposite $\angle s$]
$\Rightarrow x+{15}^0=2\left(25\right)+{25}^0$ [using (1)]
$\Rightarrow x+{15}^0={50}^0+{25}^0$
$\Rightarrow x={75}^0-{15}^0$
$\Rightarrow x={60}^0$.(in degrees)