Question

In the given diagram, AB is parallel to PQ. If a right triangle can be constructed with $\angle P{O}^{\prime }X$ and $\angle BOY$ as two of its angles, then find the value of $\angle P{O}^{\prime }X$.

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is C

${45}^{\circ }$

We know that, one of the angles of a right angled triangle is 90° ...(i)

Given that a right triangle can be formed with $\angle P{O}^{\prime }X$ and $\angle BOY$ as two of its angles.

In the given figure, $\angle P{O}^{\prime }X$ = $\angle BOY$ (Alternate interior angles) ...(ii)

For any triangle, the sum of all the interior angles is ${180}^{\circ }$ ...(iii)

From (i) and (iii),
$\angle P{O}^{\prime }X+\angle BOY+{90}^{\circ }={180}^{\circ }$
$\angle P{O}^{\prime }X+\angle BOY={90}^{\circ }$.

From (ii),
$\angle P{O}^{\prime }X$ and $\angle BOY$ are equal,
$2\times \angle P{O}^{\prime }X=90°$
$\angle P{O}^{\prime }X=45°$