Question

The supplement of an angle is four times the complement of the angle. Find the angle.
14. 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:

$\huge\fbox\red{\fbox\green{Done \: by \: Aritra \: Kar}}$

Step-by-step explanation:

1) Let, the angle be x

By The Problem:-

(180-x)=4(90-x)

or, 180-x=360-4x

or, 4x-x=360-180

or, 3x=180

or, x=60°

Answer=60°

2) Let, the angle be x

and let, it's supplementary angle be (180-x)

By The Problem:-

x:(180-x)=5:1

or,$\frac{x}{180 - x} = \frac{5}{1} \\ or ,\: x = 900 - 5x \\ or, \: 6x = 900 \\ or ,\: supplementary\: angle \: = \: \frac{900}{6} \\ = > 150\\ or, x= 150/5=30°(ans)$