Question

Find the angle whose complement is 1/3 of its supplement

Answer 1

Answer:

$\large \underline{\boxed{\mathsf{Angle\: =45^{\circ}}}}$

Step-by-step explanation:

$\underline{\underline{\textbf{Given That...}}}$

Complement angle on angles is 1/3 of its supplement we need to find the angle.

$\underline{\underline{\textbf{Solution...}}}$

Now let

The angle be x

We know

$\bigstar \textsf{Complement angles - Pair of angles who's sum = 90 deg}$

$\bigstar \textsf{Supplement angles - Pair of angles who's sum = 180 deg}$

Thus

Complement angle of x = 90 - x

Supplement angle of x = 180 - x

Therefore According to Questions

Complement angle is 1/3 of supplement angle thus we have

$\mathsf{90^{\circ} - x = \dfrac{1}{3}( 180^{\circ}- x)}$

$\implies \mathsf{90^{\circ} - x = 60^{\circ} - \dfrac{x}{3}}$

$\implies \mathsf{90^{\circ} - 60^{\circ} = -\dfrac{x}{3} + x}$

$\implies \mathsf{\dfrac{-x + 3x }{3} = 30^{\circ}}$

$\implies \mathsf{\dfrac{2x}{3} = 30^{\circ}}$

$\implies \mathsf{2x = 30^{\circ} \times 3}$

$\implies \mathsf{x = \dfrac{90^{\circ}}{2} = 45^{\circ}}$

$\underline{\textbf{Therefore required answer is}}$

$\underline{\boxed{\mathsf{ Angle \: = 45^{\circ}}}}$