Question

find the angle whose complement is two third of its supplement?

Answer 1

Given

• An angle : Complement = 2/3 of supplement

To find

• The angle

Solution

☯ According the question :

• 90° - x° = 2/3 (180° - x°)
• 3(90 - x)° = 2(180° - x°)
• 270 - 3x° = 360 - 2x°
• -90 = -2x + 3x
• -90 = x°

☯ ∴ The angle whose complement is two third of its complement is -90°

Answer 2

Answer:

270°

Step-by-step explanation:

A complement is 90° - the angle (the angle that forms 90° when paired with the given angle) and a supplement is 180° - the angle.

Let the solution be x.

(90° - x) = $\frac{2}{3\\}$(180° - x) Multiplying both sides by3,

3(90°-x) = 2(180° - x) Simplifying the brackets,

270° - 3x = 360° - 2x Adding 2x to both sides,

270° - x = 360°

270° - 360° = x

-90° = x, but an angle is same as itself added to 360°, a full rotation.

270°