Question

In the given figure, lines $AB$ and $CD$ intersect at $O.$ Find the value of $x+y$.

• A. ${72}^{\circ }$
• B. ${85}^{\circ }$
• C. ${95}^{\circ }$
• D. ${88}^{\circ }$

Answer 1

The correct option is A 72
Consider the straight line $COD.$ Since the angles on a straight line equals 180${}^{\circ }$, we have
$\angle COB+\angle BOD={180}^{\circ }$
$\Rightarrow x^{\circ }+4x^{\circ }={180}^{\circ }$
$\Rightarrow 5x^{\circ }={180}^{\circ }$
$\Rightarrow x={36}^{\circ }$
Now, note that $\angle AOD=\angle COB$ [vertically opposite angles]
$\because y=x={36}^{\circ }$
$\therefore y+x={36}^{\circ }+{36}^{\circ }={72}^{\circ }$