Chapter 2, Problem 1RP

To determine

To prove: In the given figure $\angle JKO$ is complement to $\angle OKM$

Explanation of Solution

Given information : In the given figure $\overline{JK}\perp \overline{KM}$ also $\angle JKO\text{ , }\angle OKM$ are adjacent angles.

Formula used : Rule of adjacent angles and complementary is used.

Proof: As per the given figure and information we deduce following things:

  $\overline{JK}\perp \overline{KM}\Rightarrow \angle JKM\text{ = 90}°\mathrm{...........................................}\text{(i)}$

As $\angle JKO\text{ , }\angle OKM$ are adjacent angles, and together add up to $\angle JKM$ .This relation can be expressed as:

  $\begin{array}{l}\angle JKO\text{ + }\angle OKM\text{ = }\angle JKM\\ \\ \Rightarrow \angle JKO\text{ + }\angle OKM\text{ = 90}°\mathrm{....................................}\text{(from (i))}\end{array}$

As both $\angle JKO\text{ , }\angle OKM$ add up to $90°$ ,using definition of complementary angles both the angles are complementary to each other.

Which proves the required result.