Ask Question
7 July, 13:14

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

+3
Answers (1)
  1. 7 July, 14:39
    0
    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°
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “The ratio of two supplementary angles is 2:7. What is the measure of the smaller angle? ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers