Question

angle A and angle b are complementry angles . the ratio of angle A and angle B is 4 . find the measure of angle A And angle b​

Answer 1

Answer:

Let the required angle be x

Then according to the question,

⇒

180

o

−x

90

o

−x

=

4

1

⇒ 4(90

o

−x)=180

o

−x

⇒ 360

o

−4x=180

o

−x

⇒ 360

o

−180

o

=−x+4x

⇒ 180

o

=3x

⇒ x=

3

180

o

∴ x=60

o

∴ The required angle is 60

o

.

hope it helps you

Answer 2

Answer:

The measure of the angles ∠A and  ∠B = 72° and 18°

Step-by-step explanation:

Given,

∠A and ∠B are complementary angles.

The ratio of ∠A and ∠B is 4.

To find,

The measure of ∠A and ∠B

Recall the concept:

If the sum of two angles is 90°, then the two angles are said to be complementary angles

Let us take ∠A  = x, since the angles ∠A and ∠B  are complementary we have

∠A + ∠B  = 90

x + ∠B  = 90

∠B = 90 - x

Hence the angles are x and 90 -x

Since the ratio of the two angles is 4 we have,

x : 90 -x = 4:1

$\frac{x}{90 - x} = \frac{4}{1}$

Cross multiplying we get

x = 4(90-x)

x = 360 -4x

x+4x = 360

5x = 360

x = $\frac{360}{5}$

= 72

x = ∠A = 72°

∠B = 90 -x = 90 - 72 = 18°

Answer

The measure of the angles ∠A and  ∠B = 72° and 18°

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