**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°**