help with angles?

3rd angle = 10 + 2nd angle

first angle = x

2nd angle = y

3rd angle = z

y= 2x

z=10 + 2x

x + 2x + 10 + 2x = 180 <---total degrees in a triangle 5x + 10=180 5x=170 x=34 1st=34 2nd=68 3rd=78

a + b + c = 180

We know that the second angle (b) is twice the measure of the first angle (a), or…

2a = b

And we know that the third angle (c) is ten degrees more than the measure of the second, or…

b+10 = c

Substituting for the value of b gives us

2a + 10 = c

Now we put everything back into the original equation:

a + b + c = 180

a + (2a) + (2a + 10) = 180

a + 2a + 2a + 10 = 180

5a + 10 = 180

5a = 170

a = 34 {Solution}

Then we check the answer.

a = 34

b = 2a = 68

c = b + 10 = 78

34 + 68 + 78 = 180

2nd angle = b

3rd angle = c

all 3 angles total 180: a + b + c = 180

Now, write down what you know:

b = 2a

c = b+10

* * * * * * * don’t read any further until you try it yourself, or you won’t learn it!

Substitute so you get all “a” in the equation:

a + 2a + (b + 10) = 180 therefore

a + 2a + 2a + 10 = 180

5a + 10 = 180

Now, solve for a

a = 34 degrees

b = 68 degrees

c = 78 degrees

total a + b + c = 180