Mathematics 8 Online
OpenStudy (anonymous):

This is my math problem: I a triangle ABC, angle B is 3 times angle A and angle C is 2degrees less than 6 times angle A. Find the size of the angles. ? Can anyone solve this in equation steps?

OpenStudy (sandra):

right, so this is a problem where you have three variables (the three angles), and so you'll need three equations to solve it

OpenStudy (sandra):

so let's write down three equations

OpenStudy (sandra):

1. B = 3A

OpenStudy (sandra):

2. C = 6A - 2

OpenStudy (sandra):

so there's one equation that's true for all triangles

OpenStudy (sandra):

3. A+B+C = 180 (the sum of all angles in a triangle is always 180 degrees)

OpenStudy (sandra):

now what you need to do is substitute until you get an equation with all one variable

OpenStudy (sandra):

how about let's try and get all A's

OpenStudy (sandra):

so we know B=3A, and C=6A - 2

OpenStudy (sandra):

so let's substitute both of those into the third equation - A+B+C = 180

OpenStudy (sandra):

so A + (3A) + (6A-2) = 180

OpenStudy (sandra):

10A - 2 = 180

OpenStudy (sandra):

10A = 182

OpenStudy (sandra):

A = 18.2

OpenStudy (sandra):

now that you have the value of A, you need to substitute it back into other equations to get B and C

OpenStudy (sandra):

if you do that, you'll have the answer

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