Solving for the measurements of Complementary Angles
Answer:
[tex]24.9^{\circ}[/tex] and [tex]65.1^{\circ}[/tex]
Step-by-step explanation:
Recall that Angles that are complementary to each other add up to [tex]90^{\circ}[/tex].
Let [tex]a[/tex] be the measure of the complementary angle.
If an angle is [tex]40.2^{\circ}[/tex] more than its complementary angle, the measure of that angle is [tex]a +40.2[/tex]. The sum of both angles are expressed [tex]a +(a +40.2)[/tex] but since the have to add to [tex]90[/tex] as they are complementary, [tex]a +(a +40.2) = 90[/tex].
Solving for [tex]a[/tex]:
[tex]a +(a +40.2) = 90 \\ a +a +40.2 = 90 \\ 2a +40.2 = 90 \\ 2a +40.2 -40.2 = 90 -40.2 \\ 2a = 49.8 \\ \frac{2a}{2} = \frac{49.8}{2} \\ a = 24.9[/tex]
Since the other angle measures [tex]a +40.2[/tex], we can plug in the value of [tex]a[/tex] to find the measure of the angle.
Evaluating [tex]a +40.2[/tex]:
[tex]a +40.2 \\ 24.9 +40.2 \\ 65.1[/tex]
The measure of the angles are [tex]24.9^{\circ}[/tex] and [tex]65.1^{\circ}[/tex]
