Question

(i) Find measure of an angle which is 20° less than its complement.
(ii) Find the measure of the angle, which is four times it's complement.​

Answer 1

Step-by-step explanation:

i)x and y are complementary angles, so, x+y = 90

y = 90 - x

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"An angle is 20 degrees less than its complement" which means x = y - 20

x = y - 20

x = (90-x) - 20 ... plug in y = 90-x

x = 90-x-20

x = -x+70

x+x = 70

2x = 70

x = 70/2

x = 35

The angle is 35 degrees (the complement is 90-35 = 55 degrees)

ii) Let the angle be x∘. Then it's complement = (4x)∘.

We know that if the sum of two angles is equal to 90∘ then the angles are said to be complementary.

4x+x=90∘

⇒5x=90∘

⇒x=90∘/5

⇒x=18∘

Hence, the angle = 180∘ and its complement = (4×18∘)=72∘

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Answer 2

Answer:

The measure of an angle which is 20° less than its complement : 55°

The measure of the angle, which is four times it's complement : 72°

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Step-by-step explanation:

The measure of an angle which is 20° less than its complement :

Let the angle be x

x - 20 = ( 90 - x )

2x = 90 + 20

2x = 110

x = 55°

• The measure of the angle, which is four times it's complement :

Let the angle be x

x = 4 (90° - x)

x = 360 - 4x

5x = 360

x = 360/5

x = 72°