Question

An angle is five times its complement. Find its measure.
Two supplementary angles are in the ratio 3 : 2. Find the measure​

Answer 1

Hey there!

(i) Let the measure of given angle be x  

Then, its complement is 90 −

x=5(90−x)

6x=450

x=75  

Hence, the measure of the given angle is 75 degrees.

(ii) Let the measures of the given angles be (3x) and (2x) respectively.

Since the given angles are supplementary, we have

⇒3x+2x=180

⇒5x=180

⇒x=36.

∴ the measures of the given angles are (3×36) and (2×36) i.e., 108∘ and 72∘ respectively.

Hope this helps..