1. **State the problem:** We are given a triangle ABC with AB = CB, angle ABC = 50°, and the bearing of B from A is 070°. We need to find the bearing of C from A. 2. **Understand the problem:** Since AB = CB, triangle ABC is isosceles with AB = CB. The angle at B is 50°, so the base angles at A and C are equal. 3. **Use the properties of isosceles triangles:** The sum of angles in triangle ABC is 180°, so the angles at A and C are each: $$\frac{180^\circ - 50^\circ}{2} = \frac{130^\circ}{2} = 65^\circ$$ 4. **Determine the direction of C from B:** The angle at B is 50°, which is the angle between AB and CB. Since the bearing of B from A is 070°, the line AB points at 070° from A. 5. **Calculate the bearing of C from B:** Because AB = CB and angle ABC = 50°, the line BC makes a 50° angle with AB at B. Since AB points from A to B at 070°, the line BC from B to C is at an angle of 50° from AB. The bearing of C from B is therefore: $$070^\circ + 50^\circ = 120^\circ$$ 6. **Calculate the bearing of C from A:** To find the bearing of C from A, we add the bearing of B from A (070°) and the angle at A (65°) because the triangle is isosceles and the angle at A is 65°. So the bearing of C from A is: $$070^\circ + 65^\circ = 135^\circ$$ **Final answer:** The bearing of C from A is **135°**.