Question

Find the value of x A)30 B)60 C)90 D)120

Answer 1

The value of x is 30

2×30=60°
90-30=60°
90+30=120°

Answer 2

Answer:  The correct option is (A) 30.

Step-by-step explanation:  We are given to find the value of x from the figure shown with two intersecting lines.

As noted from the figure, since the measures of two vertically opposite angles are equal, so

$2x^\circ=(y-x)^\circ\\\\\Rightarrow 2x=y-x\\\\\Rightarrow 2x+x=y\\\\\Rightarrow y=3x~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

And, from the measure of a straight angle, we can write

$2x^\circ+(y+x)^\circ=180^\circ\\\\\Rightarrow 2x+(y+x)=180\\\\\Rightarrow 3x+y=180\\\\\Rightarrow 3x+3x=180~~~~~~~~~~~~\textup{[putting the value of y from equation (i)]}\\\\\Rightarrow 6x=180\\\\\Rightarrow x=30.$

Thus, the required value of x is 30.

Option (A) is CORRECT.