Complementary angles are angles that sum up to 90 degrees.
Given the ratio of two complementary angles:
4 : 5
Where, smaller ratio = 4
larger ratio = 5
To find the measure of each angle first find the total ratio:
Total ratio = 4 + 5 = 9
• Measure of smaller angle =
[tex]\frac{\text{smaller ratio}}{\text{toal ratio}}\times90[/tex]
[tex]\frac{4}{9}\times90=40\text{ }[/tex]
The measure of the smaller angle is 40 degrees.
• Measure of larger angle =
[tex]\begin{gathered} \frac{\text{larger ratio}}{total\text{ ratio}}\times90 \\ \\ =\frac{5}{9}\times90=50 \end{gathered}[/tex]
The measure of the larger angle is 50 degrees
ANSWER:
Smaller angle = 40°
Larger Angle = 50°
