SOLUTION: A triangle has three angles, R, S, and T. Angle T is 40° greater than angle S. Angle R is 8 times angle S. What is the measure of each angle?

Algebra ->  Triangles -> SOLUTION: A triangle has three angles, R, S, and T. Angle T is 40° greater than angle S. Angle R is 8 times angle S. What is the measure of each angle?       Log On


   

Question 118543: A triangle has three angles, R, S, and T. Angle T is 40° greater than angle S. Angle R is 8 times angle S. What is the measure of each angle?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Angle T+is 40%B0° greater than angle S
=> T+=+S+%2B+40

Angle R is 8+times angle S
=> +R+=+8S+

What is the measure of each angle?
The sum of all three angles is 180°
+T+%2B+S+%2B+R+=+180……..substitute T and R
+%28S+%2B+40%29+%2B+S+%2B+8S+=+180° ……..
+10S+%2B+40=+180……..
+10S+=+180-+40……..
+10S+=+140+……..
+S+=+140%2F10+……..
+S+=+14° ……..
Now find T and R

T+=+S+%2B+40
T+=+14+%2B+40

T+=+54+°


+R+=+8S+
+R+=+8%2814%29+
+R+=+112°

Check the sum:
+T+%2B+S+%2B+R+=+180……..
+54+%2B+14%2B+112=+180……..
+180+=+180° ……..