Question

If a pair of supplementary angles are in the ratio 4:5, then find the measure of smaller angle. A) 60° B) 100° C) 20° D) 80°

Answer 1

Answer:

80

Step-by-step explanation:

4:5 ,

4x + 5x = 180

9x = 180

x=180/9

x=20

4x = 20 * 4 = 80

5x = 20*5 = 100

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Answer 2

★ ANSWER ★

• D) 80° (✔)

GIVEN:

• A pair of supplementary angles are in the ratio 4:5.

TO FIND:

• What is the measure of smaller angle ?

SOLUTION:

Let 'x' be the common in given ratios

• Larger angle = 5x
• Smaller angle = 4x

✍ We know that, the sum of supplementary angles is 180°

According to question:-

$\sf{\longmapsto 4x + 5x ={180}^{\circ}}$

$\sf{\longmapsto 9x = {180}^{\circ}}$

$\sf{\longmapsto x = \cancel\dfrac{180}{9}}$

$\bf{\longmapsto x = 20 }$

• Value of 'x' = 20

Put the value of 'x' in the given Ratios

❐ Larger angle = 5(20) = 100°

❐ Smaller angle = 4(20) = 80°

❝ Hence, the measure of smaller angle is 80° ❞

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