Given: isosceles triangle def. the measure of vertex angle d is four times the measure of each base angle e and f.

find the measures of angles d, e, and f.

measure of angle d =

degrees.

measure of angle b =

degrees.

measure of angle c =

degrees.

Step-by-step explanation:

The ratios of the measures of the angles are ...

  D : E : F = 4 : 1 : 1

The sum of ratio units is 6, so each must stand for 180°/6 = 30°. Then the ratios of actual angles are found by multiply the ratio units by 30°:

  D : E : F = 120° : 30° : 30°

Angle D is 120°; angles E and F are each 30°.

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."

yes

step-by-step explanation: