Question

An angle measures 149.2° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Solving for the measurements of Complementary Angles

Answer:

`15.4^(\circ)` and
`164.6^(\circ)`

Explanation:

Recall that Angles that are supplementary to each other add up to
`180^(\circ)`.

Let
`a` be the measure of the supplementary angle.

If an angle is
`149.2^(\circ)` more than its supplementary angle, the measure of that angle is
`a +149.2`. The sum of both angles are expressed
`a +(a +149.2)` but since the have to add to
`180` as they are supplementary,
`a +(a +149.2) = 180`.

Solving for
`a`:

`a +(a +149.2) = 180 \\ a +a +149.2 = 180 \\ 2a +149.2 = 180 \\ 2a +149.2 -149.2 = 180 -149.2 \\ 2a = 30.8 \\ (2a)/(2) = (30.8)/(2) \\ a = 15.4`

Since the other angle measures
`a +149.2`, we can plug in the value of
`a` to find the measure of the angle.

Evaluating
`a +149.2`:

`a +149.2 \\ 15.4 +149.2 \\ 164.6`

The measure of the angles are
`15.4^(\circ)` and
`164.6^(\circ)`