Question

Math 50 points please help!! If the measure of the complement of an angle is squared, it will equal 90 less than three times the supplement of the angle. Find the measure of the angle. Write a quadratic equation and solve by factoring. (hints: FOIL, if ax+bx+c-0, then ask yourself "what multiplies to 'c', but adds to 'b'?")

Answer 1

angle = 90-x

complement of angle = x

supplement of angle = x+90

x^2 = 3(x+90)-90

x^2 = 3x+270-90

x^2 =3x+180

x^2-3x-180=0

(x+12) (x-15)=0

x=-12 x=15

cannot have negative angle so x=15

angle = 90-15 = 75