Question

Solve the following questions:

$a .$ Write the measures of two complementary angles.

$b .$ Find the supplements of these two angles.

$c .$ Find the sum of the complementary angles and the supplementary angles.

$d .$ Repeat the above steps with some more pairs of complementary angles.

$e .$ Generalise the result.

Accepted Answer

$a .$ Complementary angles:

Two angles are complementary when their measures add up to $90$ degrees. Let's denote the measures of the two complementary angles as $A$ and $B$ . So, $A + B = 90 °$ .

$b .$ Supplementary angles:

Two angles are supplementary when their measures add up to $180$ degrees. The supplements of $A$ and $B$ are $180 - A$ and $180 - B$ , respectively.

$c .$ Sum of complementary and supplementary angles:

The sum of complementary angles $(A + B)$ is $90$ degrees, and the sum of supplementary angles $A + (180 - A) and B + (180 - B)$ is $180$ degrees.

$d .$ More pairs of complementary angles:

Let's take another pair of complementary angles $C$ and $D$ . So, $C + D = 90 °$ . The supplements of $C$ and $D$ would be $180 - C$ and $180 - D$ , respectively.

$e .$ Generalisation:

In general, for any pair of complementary angles $X$ and $Y$ , we have:

Complementary angles: $90 - X$ and $90 - Y$

Supplementary angles: $180 - X$ and $180 - Y$

Sum of complementary angles: $X + Y = 90 °$

Sum of supplementary angles: $X + (180 - X) = 180 °$ and $Y + (180 - Y) = 180 °$

Hence, the required answer is as shown above.

Try this

Jayashree Vipin Mathematics Solutions for Exercise - Try this

Questions from Try this with Hints & Solutions

Learn and Prepare for any exam you want !