Points A B C lie on a circle angle B = 60 ‘arc AB relate to arc BC in the same way as 7: 5 Find the angles of triangle ABC.

Given:
points A, B, C lie on a circle,
angle B = 60 ‘,
AB: BC = 7: 5,
Find the angle BAC, angle BAC -?
Solution:
1) Knowing that the inscribed angle is equal to half of the degree measure of the central angle, which rests on the same arc. Then the arc AC = 2 * 60 = 120 °;
2) The arc CBA accounts for 360 ° -120 ° = 240 ° from the entire circumference;
3) Let one part be x °, then the arc AB = 7 * x °, and the arc BC = 5 * x °. We know that the length of the CBA arc is 240 °. Let’s make the equation:
7 * x + 5 * x = 240;
x * (7 + 5) = 240;
x * 12 = 240;
x = 20;
4) 20 * 7 = 140 ° – arc AB;
5) 20 * 5 = 100 ° – BC arc;
6) Then the angle BAC = 1/2 * BC;
angle BAC = 1/2 * 100;
angle BAC = 50 °;
7) BCA angle = 1/2 * AB;
BCA angle = 1/2 * 140;
BCA angle = 70 °.
Answer: 50 and 70 degrees.