Angle 5 and 6 are supplements and angle 5 is 24 more than half the measure of angle 6. find the measure of each angle.

Supplementary angles equal 10 degrees.

Let angle 6 = X

Angle 5 is 24 more than half of angle 6, which can be written as 1/2X +24

So now we have X  + 1/2x +24 = 180

Combine the like terms ( X  +1/2X = 1.5X)

1.5x + 24 = 180

Subtract 24 from each side:

1.5x = 156

Divide both sides by 1.5:

x = 156 / 1.5

X = 104

Angle 6 = 104 degrees.

Angle 5 = 180 - 104 = 76 degrees

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."