Circle D is shown. Angles F A E, F D E, and F B E intercept arc F E. ∠FAE measures 72°. What other angle must measure 72°? ∠BFD
2 answers:
Answer:
Option D, ∠FBE
Step-by-step explanation:
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Solution
As per the property of arc, angles subtended by the same arc (chord) on the circumference of a circle have equal measures.
∠FAE is an angle subtended by the arc FE that touches the circle at point 'A'.
∠FBE is also subtended by the arc FE at the point 'B'.
Therefore, we must have
m∠FAE = m∠FBE.
Since, m∠FAE = 72°, so m∠FBE = 72°.
Hence, option D, ∠FBE
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