Question 87623: Please i need help on this question:
If one angle of a triangle is tree times a second angle and the third angle is 20 degrees more than the second angle, the SECOND ANGLE is.....
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let the angles be A, B, and C.
From the problem description, you can write:
A = 3B "One angle is 3 times a second."
C = B+20 "The third angle is 20 degrees more than the second angle."
So, we are looking for the measure of angle B, the second angle.
You already are aware that, in any triangle, the sum of the angles is 180 degrees, so you can write:
A + B + C = 180 Now substitute for A and C their equivalent values from above:
(3B) + B + (B+20) = 180 Simplify and solve for B.
5B + 20 = 180 Subtract 20 from both sides.
5B = 160 Divide both sides by 5.
B = 32 degrees.
Check:
A+B+C = 180
3(32)+32+(32+20) = 180
96+32+52 = 180
180 = 180 Check!
|
|
|
