In a triangle, the second angle is twice the measure of the first, and the third angle is three times the measure of the second. Find the measure of the third angle.
I LOVE THESE!!! Okay so lets give the angles variables Let angle 1 = A Let angle 2 = B Let angle 3 = C So we know that A+B+C= 180 because the angles of a triangle add up to 180. Also, we know that Angle 2 is twice the measure of angle 1 this means that B=2A Lastly, we know that angle 3 is three times the measure of angle 2. Therefore C=3B. If we put these all together. 1) A+B+C=180 2) B=2A 3) C=3B If we multiply both sides of equation 2 by three, we get 3B=6A and since C=3B, C=6A Now, we want to substitute these values in for B and C (Into the first equation) A+2A=6A=180 9A=180 A=20 Angle 1= 20 degrees Since we know that angle 1 = 20 degrees and angle 3 is 6 times angle 1, C= 6*20 C=120 The third angle is 120 degrees. Let me know if I helped! Comment if I didn't and I'll try to clarify things.