Subjects geometry

Central Angle 5B708C

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1. **State the problem:** We need to find the central angle $x$ in a circle given an inscribed angle of $70^\circ$ that subtends the same arc. 2. **Recall the rule:** The central angle subtending an arc is twice the inscribed angle subtending the same arc. This is a fundamental property of circles. 3. **Write the formula:** $$x = 2 \times \text{inscribed angle}$$ 4. **Substitute the given value:** $$x = 2 \times 70^\circ$$ 5. **Calculate:** $$x = 140^\circ$$ 6. **Conclusion:** The central angle $x$ is $140^\circ$. Therefore, the correct answer is option a. $140^\circ$.