1. **Problem statement:** We have a circle with points F, G, H, and D on it. F and H lie on a horizontal diameter, with F on the left and H on the right. G is at the top of the circle, and D is at the bottom. The angle at H between the horizontal diameter (H-F line) and segment H-G is 34°. We need to find the measure of the arc from F to G (denoted as ?). 2. **Key facts and formulas:** - The angle formed by two chords intersecting on the circle is half the measure of the intercepted arc. - The angle at the circumference subtended by a diameter is a right angle (90°). - The angle at H between the diameter and segment H-G is given as 34°. 3. **Step-by-step solution:** - Since F-H is a diameter, the arc F-H is 180°. - The angle at H between the diameter and segment H-G is 34°, so the angle between chord H-G and the tangent at H is 34°. - The inscribed angle theorem states that the angle at the circumference is half the measure of the intercepted arc. - The angle at H intercepts the arc F-G (the arc we want to find). - Therefore, the measure of arc F-G is twice the angle at H: $$\text{arc } FG = 2 \times 34^\circ = 68^\circ$$ 4. **Final answer:** The measure of the arc from F to G is **68 degrees**.