The second angle of a triangle is 2 times as large as the 1st.?

Question

The 3rd angle is 10 degrees more than the 2nd angle. find the measure of the 1st angle." in Yahoo! Answers

Answer 1

The three angles of a triangle add to 180 degrees.

So...

x + 2x + (2x+10) = 180

5x = 170

x = 34

Angle 1 = 34 degrees
Angle 2 = 68 degrees
Angle 3 = 78 degrees

Check: 34 + 68 + 78 = 180

Answer 2

a + b + c = 180
where a = 1st angle, b = 2nd angle, c = 3rd angle

we also know:
b = 2a
and
c = b + 10

now you have 3 equations and 3 unknowns:

solve the 2nd eqn for a: a = (b/2)
plug a = b/2 and c = b + 10 in the first eqn:
(b/2) + b + b + 10 = 180
multiply everything by 2:
b + 2b + 2b + 20 = 360
5b = 340
b = 68 degrees

we know:
b = 2a:
68 = 2a
a = 34 degrees

c = b + 10:
c = 68 + 10 = 78 degrees.

check: 34 + 68 + 78 = 180.

ANS: a = 1st angle = 34 degrees.

Answer 3

Well, all the angles of a triangle have to add to 180 degrees. Subtract 10 and you get 170, divide by 5 and you get 34. You can check this:
Angle 1 = 34
Angle 2 = 34*2=68
Angle 3 = 68+10=78
34+68+78=180
So your answer is 34.

Answer 4

Let the 1st angle=x
the 2nd angle=2x
the 3rd angle=2x+10degrees
their sum=5x+10=180
5x=170
x=34degrees ANS

Answer 5

Let "a" be the "first" angle. Use the fact from geometry that the sum of the angles in any triangle is always 180 degrees.

That means:

(first angle) + (second angle) + (third angle) = 180

or:

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

Now just solve for "a".

Answer 6

let x be 1st angle, 2nd is 2x, 3rd is 2x+10, and all 3 add up to 180, so

x + 2x + 2x+10 = 180
5x = 170
x = 34
2x = 68
2x+10 = 78

Answer 7

x + 2x + 2x + 10 = 180

5x + 10 = 180
5x = 170
x = 34

Angle 1 = 34
Angle 2 = 68
Angle 3 = 78

Answer 8

angles called A, B, and C

A + B + C = 180
B = 2A
C = B + 10 = 2A + 10

A + B + C = 180
A + (2A) + (2A+10) = 180
A + 2A + 2A +10 = 180
5A + 10 = 180
5A = 170
A = 170 / 5
A = 34