ANSWER
58°
EXPLANATION
The relationship between the measure of the bigger arc and the smaller arc and the angle created by the secant and the tangent is
[tex]51 \degree = \frac{1}{2} (160 - x)[/tex]
Multiply through by 2
This implies that
[tex]2 \times 51 \degree =2 \times \frac{1}{2} (160 - x)[/tex]
We simplify to get:
[tex]102 \degree =160 - x[/tex]
Solve for x.
[tex]102 \degree - 160 \degree =- x[/tex]
[tex] - 58 \degree =- x[/tex]
[tex]58 \degree =x[/tex]
