Five times the complement of an angle less twice the angle's supplement is 450. How do you find the the measure of the supplement?

Question

Evelyn Arboleda · Accepted Answer

Please Check the Problem.

Suppose that, the reqd. measure of the angle is #x.# Then, its Complement measures #(90-x),# whereas, the Supplement, #(180-x).# By what is given, we have, # 5(90-x)-2(180-x)=450.# #:. cancel450-5x-360+2x=cancel450.# #:. -3x=360, or, x=-120,# which is not possible, as #x # can not be #-ve.#

Carson Arnold · Answer

undefined Let $ x $ be the measure of the angle.

The complement of the angle is $ 90^\circ - x $.

The supplement of the angle is $ 180^\circ - x $.

According to the given condition, we have:

$$ 5(90^\circ - x) - 2(180^\circ - x) = 450 $$

Solving this equation for $ x $:

$$ 450 - 5(90^\circ) + 2(180^\circ) = 450 $$

$$ 450 - 450 + 360 - 2x = 450 $$

$$ 360 - 2x = 450 $$

$$ -2x = 450 - 360 $$

$$ -2x = 90 $$

$$ x = \frac{90}{-2} $$

$$ x = -45^\circ $$

Since the supplement of an angle is always positive, we consider $ 180^\circ - x $:

$$ 180^\circ - (-45^\circ) = 180^\circ + 45^\circ = 225^\circ $$

Therefore, the measure of the supplement is $ 225^\circ $.