Question

1.The supplement of an angle is four times the complement of the angle. Find the angle.
2.The ratio of an angle and its supplement is 5: 1. Find the angle.​

Answer 1

Question 1

The supplement of an angle is four times the complement of the angle. Find the angle.

Solution

Given

Supplementary Angle is four times the complement of an angle

To Find

The angle

Steps

Supplementary means 180° & Complementary means 90°

✭ The Angles

→ (180-x) = 4(90-x)

→ 180-x = 360-4x

→ 180-360 = -4x+x

→ -180 = -3x

→ -180/-3 = x

→ x = 60°

Question 2

The ratio of an angle and its supplement is 5:1. Find the angles.

Solution

Given

Supplementary Angles are of the ratio 5:1

To Find

The angles

Steps

We know that here the angles would add up to 180°

Assume the angles as 5x & x

✭ Value of x

→ 5x+x = 180°

→ 6x = 180°

→ x = 180/6

→ x = 30°

✭ The Angle

5x = 5×30 = 150°

x = 30°

Answer 2

Answer:

Solution ❶

Given :-

The supplement of an angle is four times the complement of the angle.

To Find :-

What is the angle.

Solution :-

Let, the angle be x

Supplement angle = 180° - x

And, complement angle = 90° - x

According to the question,

⇒ (180° - x) = 4(90° - x)

⇒ 180° - x = 360° - 4x

⇒ - x + 4x = 360° - 180°

⇒ 3x = 180°

⇒ x = $\sf\dfrac{\cancel{180°}}{\cancel{3}}$

➠ x = 60°

∴ The angle is 60° .

Solution ❷

Given :-

The ratio of an angle and its supplement is 5:1.

To Find :-

What is the angle.

Solution :-

Let, the ratio be 5x : x

And, the sum of supplement angle is 180°

According to the question,

⇒ 5x + x = 180°

⇒ 6x = 180°

⇒ x = $\sf\dfrac{\cancel{180°}}{\cancel{6}}$

➠ x = 30°

Hence, the required angles are,

➣ First angle = 5x = 5(30°) = 150°

➣ Second angle = x = 30°