Solving for the measurements of Complementary Angles
Answer:
[tex]15.4^{\circ}[/tex] and [tex]164.6^{\circ}[/tex]
Step-by-step explanation:
Recall that Angles that are supplementary to each other add up to [tex]180^{\circ}[/tex].
Let [tex]a[/tex] be the measure of the supplementary angle.
If an angle is [tex]149.2^{\circ}[/tex] more than its supplementary angle, the measure of that angle is [tex]a +149.2[/tex]. The sum of both angles are expressed [tex]a +(a +149.2)[/tex] but since the have to add to [tex]180[/tex] as they are supplementary, [tex]a +(a +149.2) = 180[/tex].
Solving for [tex]a[/tex]:
[tex]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 \\ \frac{2a}{2} = \frac{30.8}{2} \\ a = 15.4[/tex]
Since the other angle measures [tex]a +149.2[/tex], we can plug in the value of [tex]a[/tex] to find the measure of the angle.
Evaluating [tex]a +149.2[/tex]:
[tex]a +149.2 \\ 15.4 +149.2 \\ 164.6[/tex]
The measure of the angles are [tex]15.4^{\circ}[/tex] and [tex]164.6^{\circ}[/tex]
