The smallest angle in a triangle is 64 degrees less than the  TOPIC_SOLVED

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The smallest angle in a triangle is 64 degrees less than the

Postby buddy on Fri Apr 10, 2009 5:11 pm

i need to know how to set up an equation for this: The smallest angle in a triangle is 64 degrees less than the largest angle. The remaining angle is 8 degrees more than thesmallest angle. What is the measure of each angle? help?
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Postby stapel_eliz on Fri Apr 10, 2009 8:46 pm

buddy wrote:i need to know how to set up an equation for this: The smallest angle in a triangle is 64 degrees less than the largest angle. The remaining angle is 8 degrees more than thesmallest angle. What is the measure of each angle?

Start by naming things:

i) The smallest angle is defined in terms of the largest, so pick a variable to stand for the measure of the largest angle.

ii) In terms of the variable in (i), create an expression to stand for the measure of the smallest angle, being the measure of the largest angle, less sixty-four.

iii) In terms of the expression in (ii), create an expression for the measure of the middle-sized angle, being the measure of the smallest angle, plus eight.

iv) Sum the variable in (i) and the expressions in (ii) and (iii). Set the result equal to the angle-sum for any triangle.

v) Solve the equation you created in (iv).

vi) Back-solve for the requested information, using your definitions in (i), (ii), and (iii).

If you get stuck, please reply showing how far you have gotten. Thank you! :D
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Re: The smallest angle in a triangle is 64 degrees less than the

Postby buddy on Mon Apr 13, 2009 9:31 pm

is this rite?

i) A
ii) A-64
iii) A-64+8
iv) A+A-64+A-64+8=180
v) 3A-120=180 3A=300 A=100
vi) A-64=46,46+8=52

thnx
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  TOPIC_SOLVED

Postby stapel_eliz on Thu Apr 16, 2009 2:17 pm

You can check the answer to any "solving" exercise by plugging your solution back into the original problem. First, though, you need to clearly state what that answer is! :wink:

It would appear that you have arrived at the following solution:

. . . . .largest angle: 100 degrees
. . . . .smallest angle: 46 degrees
. . . . .middle angle: 52 degrees

Do these values add up to the proper sum?

. . . . .100 + 46 + 52 = 198

Oops! That can't be right! :oops:

Checking your steps:

. . . . .largest: A
. . . . .smallest: A - 64
. . . . .middle: (A - 64) + 8 = A - 56

. . . . .angle sum: A + (A - 64) + (A - 56) = 180

. . . . .3A - 120 = 180
. . . . .3A = 300
. . . . .A = 100

So that part looks good. Now solve for the other angle measures:

. . . . .smallest: 100 - 64 = 36
. . . . .middle: 36 + 8 = 44

Does this angle sum work? :popcorn:
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