Answer:
1. ∠A = 70, ∠B = 50, ∠C = 60
2. y = 52
Step-by-step explanation:
1.
The exterior angle and the interior to that would have a SUM of 180.
So, if exterior to ∠C is 120, we can say:
exterior to C + ∠C = 180
120 + ∠C = 180
∠C = 180 - 120 = 60
∠C = 60
We also know sum of all 3 angles in a triangle is 180. Thus we can write:
∠A + ∠B + ∠C = 180
2x + x + 15 + 60 = 180
3x + 75 = 180
3x = 105
x = 105/3
x = 35
Thus,
∠A = 2x = 2(35) = 70
∠A = 70
and
∠B = x + 15 = 35 + 15 = 50
∠B = 50
2. The angle "4x" and its exterior angle "5x" is a straight line, so the sum is 180. Now, we find x:
4x + 5x = 180
9x = 180
x = 180/9
x = 20
So, we can say the angle "4x" is 4(20) = 80
We know sum of 3 angles of a triangle is 180, thus:
y + 48 + 80 = 180
y + 128 = 180
y = 180 - 128
y = 52
