Question 1196065: Question 1 options:
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is fifteen more than the second. Find the measures of the three angles.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
A = first angle
B = second angle
C = third angle
We're given that The third angle is fifteen more than the second, which means C = B+15
Also, The sum of the measures of the second and third angles is three times the measure of the first angle which means:
B+C = 3A
We'll use the fact that for any triangle, the interior angles sum to 180
A+B+C = 180
A+(B+C) = 180
A+(3A) = 180
4A = 180
A = 180/4
A = 45
So,
B+C = 3A
B+C = 3*45
B+C = 135
Now plug in C = B+15 and solve for B
B+C = 135
B+B+15 = 135
2B+15 = 135
2B = 135-15
2B = 120
B = 120/2
B = 60
Then we can find C
C = B+15
C = 60+15
C = 75
Summary:
A = 45 degrees
B = 60 degrees
C = 75 degrees
where A,B,C are the 1st,2nd,3rd angles in that exact order.
Answer by ikleyn(52824)  (Show Source):
You can put this solution on YOUR website! .
Question 1 options:
The sum of the measures of the angles of a triangle is 180.
The sum of the measures of the second and third angles is three times
the measure of the first angle.
The third angle is fifteen more than the second.
Find the measures of the three angles.
~~~~~~~~~~~~~~~~~
Let the angles be x, y, and z (the degrees measures for the 1st, 2nd and 3rd).
Then
x + y + z = 180 degrees.
Group them according the condition
x + (y + z) = 180
Replace (y + z) by 3x, since it is given. You will get
x + 3x = 180
4x = 180
x = 180/4 = 45 degrees for the 1st angle.
Thus y + z = 180 - 45 = 135, and z = y+15.
It gives y + (y+15) = 135, 2y = 135-15 = 120, y = 120/2 = 60 degrees for the 2nd angle.
Hence, z = 60+15 = 75 degrees.
ANSWER. 1st angle is 45 degrees; 2nd angle is 60 degrees; 3rd angle is 75 degrees.
Solved.
|
|
|
