Question

Five times the complement of an angle is equal to twice the supplement.

What is the angle?

What is the complement?

What is the supplement?

Answer 1

Answer:

Angle = 30 degrees, Supplement = 150 degrees, Complement = 60 degrees.

Step-by-step explanation:

Let the Angle be x.

5 (90 - x) = 2 (180 - x)

450 - 5x = 360 - 2x

450 - 360 = 5x - 2x

3x = 90

x = 90/3 = 30.

Supplement = 180 - 30 = 150

Complement = 90 - 30 = 60.

Answer 2

Given,

Five times the complement of an angle is equal to twice the supplement.

Solution,

Assume that the required angle is $\[x^\circ .\]$

Therefore,

$\[\begin{array}{l} \Rightarrow 5\left( {90^\circ - x^\circ } \right) = 2\left( {180^\circ - x^\circ } \right)\\ \Rightarrow 450^\circ - 5x^\circ = 360^\circ - 2x^\circ \\ \Rightarrow 450^\circ - 360^\circ = 5x^\circ - 2x^\circ \end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow 3x^\circ = 90^\circ \\ \Rightarrow x^\circ = \frac{{90^\circ }}{3}\\ \Rightarrow x^\circ = 30^\circ \end{array}\]$

Therefore, the complementary angle

$\[\begin{array}{l} \Rightarrow 90^\circ - 30^\circ \\ \Rightarrow 60^\circ \end{array}\]$

Similarly, the supplementary angle

$\[\begin{array}{l} \Rightarrow 180^\circ - 30^\circ \\ \Rightarrow 150^\circ \end{array}\]$

Hence, the angle, complement and supplement angle are $\[30^\circ ,60^\circ {\rm{and150}}^\circ \]$ respectively.