1. **State the problem:** We have a circle tangent to two rays from point Q, with tangent points R and P on the circle. The angle at Q is 70° and an expression 83x + 1 is given, likely representing an angle or length related to the figure. 2. **Identify what is asked:** Since the problem involves tangents and an angle at Q, and an expression 83x + 1, we likely need to find the value of $x$ or the measure of an angle related to the tangents. 3. **Recall tangent properties:** Tangents from a common external point are equal in length. 4. **Use the angle property:** The angle between two tangents from a point outside the circle is related to the intercepted arc. The angle between the tangents equals half the difference of the measures of the intercepted arcs. 5. **Set up the equation:** Given the angle at Q is 70°, and the other angle is $83x + 1$, we can write: $$70 = 83x + 1$$ 6. **Solve for $x$:** $$70 = 83x + 1$$ Subtract 1 from both sides: $$70 - 1 = 83x$$ $$69 = 83x$$ Divide both sides by 83: $$x = \frac{69}{83}$$ Show cancellation: $$x = \frac{\cancel{69}}{\cancel{83}}$$ (no common factors to cancel) 7. **Final answer:** $$x = \frac{69}{83} \approx 0.8313$$