11 points
Please help me find the value of x

166°

Step-by-step explanation:

Let's label our triangle.

We'll name the left one, next to ∠x, ∠A.

The bottom one, next to the 97°, ∠B.

And the top one, ∠C.

We know what angle ∠A is because its a supplementary angle to the 97° one.

180° - 97° = 83°

We know that the triangle is isosceles, so that gives us ∠C as well. 83°

∠A is the last remaining angle.

The sum of the angles to our ΔABC is 180°.

∠A = 180° - ∠B - ∠C

∠A = 180° - 83°- 83°

∠A = 14°

∠x and ∠A are supplementary angles!

∠x = 180° - ∠A

∠x = 180° - 14°

∠x = 166°

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."