Answer:
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°
