Chapter 5, Problem 24SGR

To determine

To prove: The assumption which make to start an indirect proof of the given statement.

Answer to Problem 24SGR

No angle is right angle.

Explanation of Solution

Given:Twoanglesare complementary angle.

Just suppose that the two complementary angles are $x$ and $y$ .

So $\angle x+\angle y={90}^0$ because of complementary angle properties.

Now consider that the conclusion is wrong by assuming its opposite is right.

Means suppose that $\angle x={90}^0$ . And if $\angle x={90}^0$ then $\angle x+\angle y>{90}^0$ which cant

be true because $\angle x+\angle y={90}^0$ thus this is a contradiction.

And similarly, $\angle y={90}^0$ can’t be possible.

Since the assumption of $\angle x={90}^0$ and $\angle y={90}^0$ leads to the contradiction which can’t

be possible in the case of complementary angle.

Hence, it is proved that neither angle is right angle.