The ratio of two supplementary angles is 2:7. What is the measure of the smaller angle?

The measure of smaller angle = 40°

Step-by-step explanation:

Supplementary Angles : Two angles P and Q are said to complementary angles if and only if they add up to a measure of 180°.

if ∠ P + ∠Q = 180° ⇒ P and Q are Complementary angles.

Now, here the ration of two angles = 2:7

Let us assume the common factor in the ratio = m

So, the measure of firs tangle - 2 x (m) = 2 m

Also, the measure of the second angle = 7 x (m) = 7 m

Also, First Angle + Second Angle = 180° (Complementary angles)

⇒2 m + 7 m = 180°

or, 9 m = 180°

⇒ m = 180 / 9 = 20

So, the common ratio m = 20

So, the first angle = 2 m = 2 x 2 = 40°

Second angle = 7 m = 7 x 20 = 140°

Hence, the measure of smaller angle = 40°