Please help with these two questions I am stuck on them.

Question

1. Gabriela had to take three tests in her accounting class. she scored 71 points on her first test and 85 points on her second test. if her average for the threes test is 83, what score did Gabriela get on her third test?

 

 

2. In a triangle, the measurement of the largest angle is 17 degrees more than twice the measure of the middle angle. The smallest angle is 5 degrees less than the measure of the middle angle. What are the measurements of the three angles?

Answer 1

1. average for 3 tests = 83; so, total points = 3 x 83 = 249 points

so, 249p - score for test 1 - score for test 2 = score for test 3

249 - 71 - 85 = 93 points

 

2. let l = largest angle, m = middle angle, and s = smallest angle

then l = 2m + 17^o, and s = m - 5^o

 

we know that sum of the angles in a triangle is 180^o

so, 2m + 17^o + m + m - 5^o = 180^o

then, 4m + 12^o = 180^o, and m = 42^o

then, l = 2(42^o) + 17^o = 101^o

and s = 42^o - 5^o = 37^o

 

checking: 101^o + 42^o + 37^o = 180^o