The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 29 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

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Explanation:

The three angles add to 180, so x+y+z = 180

The second and third angles add to 3 times the measure of the first, so y+z = 3x

The third angle is 29 more than the second, so z = y+29

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The system of equations is

For now, let's focus on the second and third equations only.

Start with y+z = 3x. Replace z with y+29 which is valid because of the third equation.

So we'll have

y+z = 3x

y+y+29 = 3x

2y+29 = 3x

Let's isolate y

2y+29 = 3x

2y = 3x-29

y = (3x-29)/2

y = 3x/2 - 29/2

y = 1.5x - 14.5

We'll use this later.

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Go back first equation of the system. Plug in z = y+29

x+y+z = 180

x+y+y+29 = 180

x+2y+29 = 180

Then plug in y = 1.5x - 14.5 we found earlier

x+2y+29 = 180

x+2(1.5x-14.5)+29 = 180

x+3x-29+29 = 180

4x = 180

x = 180/4

x = 45

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We can use this x value to find y

y = 1.5x - 14.5

y = 1.5*45 - 14.5

y = 53

and use this to find z

z = y+29

z = 53+29

z = 82

As a check, x+y+z = 45+53+82 = 180 to help confirm the answer. I'll let you check the other equations.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

answer: 2 answers

step-by-step explanation: the first one means to spread the product throughout the marketplace such that a large number of people can buy it.  

the second means the process of making a product or service available for the consumer or business user that needs it.

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