Question

12.
13.
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:

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°