The measure of angle bac is 77 and the measure of angle acd is 127, what is the measure of angle abc?

The measure of angle ABC is 50°

Step-by-step explanation:

step 1

Find the measure of angle ACB

we know that

∠ACB+∠ACD=180° ----> by supplementary angles

see the attached figure to better understand the problem

∠ACB=180°-127°=53°

step 2

Find the measure of angle ABC

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

so

∠ABC+∠ACB+∠BAC=180°

substitute the given values

∠ABC+53°+77°=180°

∠ABC=180°-130°=50°

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.