In any triangle the sum of the measures of the angles is 180. In triangle ABC, A is three times as large as B and also 16 larger than C. Find the measures of each angle.

Question

I also would like to know how to solve these problems:
In isosceles trapezoid ABCD, the longer base, AB is one and one half times as long as the shorter base, CD. The other two sides, AD and BC, are both 13 cm long. Find the lengths of AB and CD if the perimeter is 76 cm. Also, if the height of the trapezoid is 12 cm, find it's area.

In one day, Machine A caps twice as many bottles as Machine B. Machine C caps 500 more bottles than Machine A. The three machines cap a total of 40,000 bottles in a day. How many bottles does each of the machines cap in one day?

Answer 1

Let CD = x
Let AB = 1.5x

x + 1.5x + 13 + 13 = 76
Solve for x.

Area of a trapezoid = h((b1+b2)/2)
Where b1 and b2 are the two bases of a trapezoid.

For your machine question:
Let x be the number of bottles capped for machine b
Let 2x be ... machine a
Let 2x + 500 be ... machine c

x + 2x + 2x + 500 = 40000
Solve for x.

Answer 2

Triangle question:

Let x be B
Let 3x be A
Let 3x - 16

x + 3x + 3x - 16 = 180
Solve for x

Answer 3

Oh, I get it now. Thank you!

Answer 4

NP, but sorry. The "lets" for the machine and triangle questions are reversed. IE instead of "Let x be B" it's "Let B be x"

Answer 5

Angle A is 28, Angle B is 84, and Angle C is 68