In parallelogram ABCD, the measure of angle A is 99 degrees. Explain why the measure of adjacent angle B must be 81 degrees.

The measure of angle B must be 81° because angles A and B are interior supplementary angles

Step-by-step explanation:

Let us revise the properties of a parallelogram

In any parallelogram:

Let us solve our question

In parallelogram ABCD

∵ AD and BC are opposite sides

∴ AD // BC

∵ ∠A and ∠B are adjacent angles

→ That means ∠A and ∠B are interior supplementary angles

∴ ∠A and ∠B are supplementary angles

∵ The sum of the measures of the supplementary angles is 180°

∴ m∠A + m∠B = 180°

∵ m∠A = 99°

∴ 99° + m∠B = 180°

→ Subtract 99° from both sides

∴ 99° - 99° + m∠B = 180° - 99°

∴ m∠B = 81°

The measure of angle B must be 81° because angles A and B are interior supplementary angles

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(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0