1. **State the problem:** We need to find the value of angle $x$ in a circle where two diameters/chords intersect at the center, creating angles marked 52° and $x$, with two inscribed angles labeled 8°. 2. **Recall the key fact:** When two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. 3. **Identify the arcs:** The given 52° and $x$ are arcs intercepted by the chords. 4. **Use the inscribed angle theorem:** The inscribed angle is half the measure of its intercepted arc. Since the inscribed angles are 8°, the arcs they intercept are $2 \times 8 = 16°$ each. 5. **Set up the equation:** The sum of arcs intercepted by the vertical angles is $52° + x$. The inscribed angles correspond to arcs of 16°, so the sum of arcs intercepted by the vertical angles equals $16° + 16° = 32°$. 6. **Equate and solve:** $$ 52 + x = 32 $$ Subtract 52 from both sides: $$ \cancel{52} + x - \cancel{52} = 32 - 52 $$ $$ x = -20 $$ 7. **Interpretation:** A negative angle is not possible here, so re-examine the problem. Since the two inscribed angles are 8°, their intercepted arcs are 16° each, but these arcs correspond to the arcs opposite to the ones marked 52° and $x$. The total circle is 360°, so: $$ 52 + x + 16 + 16 = 360 $$ $$ 52 + x + 32 = 360 $$ $$ 52 + x = 328 $$ $$ x = 328 - 52 = 276 $$ **Final answer:** $$ x = 276° $$