Angle A is 12° greater than angle C. To find the angles of the triangle, we can use the fact that the sum of the angles in a triangle is 180°. By substituting the expressions for A and C in terms of B, we can solve for B and then find the values of A and C. The angles of the triangle are A = 84°, B = 72°, and C = 24°.
Let C be the measure of angle C. Angle A is 12° greater than angle C, so angle A is C + 12°.
The sum of the angles in a triangle is 180°. Therefore, A + B + C = 180°.
Substituting the expressions for A and C, we have (C + 12°) + B + C = 180°.
Combining like terms, we get 2C + B + 12° = 180°.
Subtracting 12° from both sides, we have 2C + B = 168°.
Since A is 12° greater than C, angle A is also 12° greater than B. Therefore, A = B + 12°.
Substituting the expression for A in terms of B, we have (B + 12°) + B + 12° = 168°.
Combining like terms, we get 2B + 24° = 168°.
Subtracting 24° from both sides, we have 2B = 144°.
Dividing both sides by 2, we find that B = 72°.
Substituting this value of B back into the equation A = B + 12°, we find that A = 84°.
Therefore, the angles of the triangle are A = 84°, B = 72°, and C = 24°.