Answer:
Angle ABC is 22 degrees
Angle BAC is 68 degrees
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Work Shown:
Because there are just 3 points, we can refer to "angle BAC" as "angle A" and "angle ABC" as "angle B". Focus on the middle letter of each three-letter sequence.
The three angles A, B, C add up to 180 degrees. This is true for any triangle.
A+B+C = 180
(6x+8) + (2x+2) + 90 = 180 ... substitution
6x+8 + 2x+2 + 90 = 180
8x+100 = 180
8x+100-100 = 180-100 ... subtract 100 from both sides
8x = 80
8x/8 = 80/8 ... divide both sides by 8
x = 10
If x = 10, then angle BAC is
angle BAC = 6x+8
angle BAC = 6*10+8
angle BAC = 60+8
angle BAC = 68
Use x = 10 to find angle ABC as well
angle ABC = 2x+2
angle ABC = 2*10+2
angle ABC = 20+2
angle ABC = 22
The three angles of this triangle are A = 68, B = 22, C = 90
As a check, the three angles must add to 180
A+B+C = 180
68+22+90 = 180
180 = 180
Answers are confirmed
Another thing to notice is that A+B = 90 meaning that A and B are complementary angles. A+B = 68+22 = 90.