Question

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles?

• A. ${45}^{\circ },{45}^{\circ },{180}^{\circ }$
• B. ${90}^{\circ },{90}^{\circ },{90}^{\circ }$
• C. ${60}^{\circ },{60}^{\circ },{90}^{\circ }$
• D. ${60}^{\circ },{90}^{\circ },{90}^{\circ }$

Answer 1

The correct option is B ${90}^{\circ },{90}^{\circ },{90}^{\circ }$

Let $AB$ and $CD$ be two lines Intersecting at $O$, such that, $\angle AOD={90}^{\circ }$
Now, $\angle AOD=\angle COB={90}^{\circ }$ (Vertically opposite angles)
$⟹\angle AOD+\angle DOB={180}^o$ (Angles on a straight line)
$⟹90+\angle DOB={180}^o$
$\angle DOB={90}^{\circ }$
$\angle DOB=\angle AOC={90}^{\circ }$ (Vertically opposite angles)
Thus, all angles are ${90}^{\circ }$.