Question
Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.
✓
Answer
Two angles, which are adjacent and supplementary, are called linear pair of angles.
Draw a line AB and mark a point O on it.
When we draw any angle $\angle\text{AOC},$ we also get another angle $\angle\text{BOC}.$
Bisect $\angle\text{AOC}$ by a compass and a ruler and get the ray OX.
Similarly, bisect $\angle\text{BOC}$ and get the ray OY.
Now,
$\angle\text{XOY}=\angle\text{XOC}+\angle\text{COY}$
$=\frac{1}2{}\angle\text{AOC}+12\angle\text{BOC}$
$=\frac{1}{2}(\angle\text{AOC}+\angle\text{BOC})$
$=\frac{1}{2}\times180^{\circ}=90^{\circ}$ (As $\angle\text{AOC}$ and $\angle\text{BOC}$ are supplementary angles)
Draw a line AB and mark a point O on it.
When we draw any angle $\angle\text{AOC},$ we also get another angle $\angle\text{BOC}.$
Bisect $\angle\text{AOC}$ by a compass and a ruler and get the ray OX.
Similarly, bisect $\angle\text{BOC}$ and get the ray OY.
Now,
$\angle\text{XOY}=\angle\text{XOC}+\angle\text{COY}$
$=\frac{1}2{}\angle\text{AOC}+12\angle\text{BOC}$
$=\frac{1}{2}(\angle\text{AOC}+\angle\text{BOC})$
$=\frac{1}{2}\times180^{\circ}=90^{\circ}$ (As $\angle\text{AOC}$ and $\angle\text{BOC}$ are supplementary angles)
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