SOLUTION: THE SECOND ANGLE OF A TRIANGLE IS TWO TIMES AS LARGE AS THE FIRST.THE THIRD ANGLE IS 10DEGREES MORE THAN THE SECOND ANGLE. FIND THE MEASURE OF THE FIRST ANGLE.

Algebra ->  Triangles -> SOLUTION: THE SECOND ANGLE OF A TRIANGLE IS TWO TIMES AS LARGE AS THE FIRST.THE THIRD ANGLE IS 10DEGREES MORE THAN THE SECOND ANGLE. FIND THE MEASURE OF THE FIRST ANGLE.      Log On


   

Question 61683This question is from textbook
: THE SECOND ANGLE OF A TRIANGLE IS TWO TIMES AS LARGE AS THE FIRST.THE THIRD ANGLE IS 10DEGREES MORE THAN THE SECOND ANGLE. FIND THE MEASURE OF THE FIRST ANGLE. This question is from textbook

Found 2 solutions by joyofmath, funmath:
Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
THE SECOND ANGLE OF A TRIANGLE IS TWO TIMES AS LARGE AS THE FIRST.THE THIRD ANGLE IS 10 DEGREES MORE THAN THE SECOND ANGLE. FIND THE MEASURE OF THE FIRST ANGLE.
Let the first angle = A.
Then, the second angle = 2A.
The third angle = 2A+10.
The 3 angles add up to 180 (for all triangles.)
So, A%2B2A%2B%282A%2B10%29+=+180.
Or, 5A%2B10+=+180.
Or, 5A=170.
Or, A=170%2F5+=+34+degrees.
Verification:
First angle = 34.
Second angle = 2*first angle = 68.
Third angle = second angle + 10 = 78.
The three angles add up to 34+68+78 = 180.

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
THE SECOND ANGLE OF A TRIANGLE IS TWO TIMES AS LARGE AS THE FIRST.THE THIRD ANGLE IS 10 DEGREES MORE THAN THE SECOND ANGLE. FIND THE MEASURE OF THE FIRST ANGLE.
Let the first angle be: x
Then the second angle is: 2x
Then the third angle is: 2x+10
Angles of triangles add to = 180
:
1st+2nd+3rd=180
(x)+(2x)+(2x+10)=180
5x+10=180
5x+10-10=180-10
5x=170
5x/5=170/5
x=34
:
The 1st angle is: x=34 degrees.
:
For fun find out the other angles too.
2nd angle: 2x=2(34)=68 degrees
3rd angle: 2x+10=2(34)+10=78 degrees.
:
Sanity Check, if you add all three angles do you get 180?
34+68+78=180 yes!!!
:
Happy Calculating!!!