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Answer:
angle BAC = 35°
Explanation:
The measure of an inscribed angle is half the measure of the arc it intercepts. Arc BC is 70°, so inscribed angle BAC is half that, or 70°/2 = 35°.
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In this geometry, you can find angle BAC a couple of ways.
Any triangle inscribed in a semicircle is a right triangle. That is, AB is a diameter, so angle ACB intercepts half the circle (180°). Half that measure is 90°. Then angles ABC and BAC are complementary:
angle BAC = 90° -55° = 35°