I NEED HELP ASAP "Find the measure of each angle in the following diagram"

Mathematics

2 answers:

weeeeeb [17]2 years ago

5 0

Answer:

Each angle is 60°

Step-by-step explanation:

The 2 angles are equal to each other because they're alternate exterior angles:

10x - 20 = 7x + 4

10x - 7x = 4 + 20

3x = 24

x = 8

10x - 20

10(8) - 20

80 - 20

Since these angles are exterior angles, their angle measures are equal so they both are 60°

Paul [167]2 years ago

4 0

60 degrees is the measurement of each angle :)

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1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

qaws [65]

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

$m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ$

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

$m\angle DOF=2m\angle OEF=64^\circ$

so the measure of arc DF is also 64 degrees. So we have

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

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

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

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

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