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Alenkinab [10]
3 years ago
12

How many 1/4 are there in 9

Mathematics
1 answer:
miv72 [106K]3 years ago
3 0

Answer:

36

Step-by-step explanation:

9÷1/4

=9×4

=36

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1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is (2x+10)^\circ, so the measure of arc DF is

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The inscribed angle theorem tells us that the central angle subtended by arc DF, \angle DOF, has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

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170-2x=64\implies106=2x\implies\boxed{x=53}

###

2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ

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m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}

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