Mathematics, 21.07.2020 21:01 windmadness5331

Study the diagram of circle C. A circumscribed angle, ∠EFG, is tangent to ⨀C at points E and G, and ∠ECG is a central angle. Point P lies on the major arc formed by points E and G. If m∠EFG=(3x+11)∘, and m∠GCE=(5x−23)∘, what are the measures of the central and circumscribed angles?

Study the diagram of circle C. A circumscribed angle, ∠EFG, is tangent to ⨀C at points E and G, and

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Answer from: deaishaajennings123

Correct answer is 4th option

$m\angle EFG=83^\circ$ , $m\angle GCE=97^\circ$

Step-by-step explanation:

Given:

There are two tangents on the circle C at the point E and G.

$m\angle EFG=(3x+11)^\circ$ , and $m\angle GCE=(5x-23)^\circ$

To find:

The value of central and circumscribed angles = ?

Solution:

First of all, let use recall a property of tangents on a circle.

The line joining the center of circle to the point on circle on which there is a tangent, make an angle of $90^\circ$ with the tangent itself.

i.e. $\angle CGF = \angle CEF = 90^\circ$ ( $\because$ G and F are the points on circle's tangent drawn from point F.)

Now, we can see that CGFE is a quadrilateral.

And sum of all internal angles of a quadrilateral is equal to $360^\circ$

$m \angle C+m \angle G+m \angle F+m \angle E = 360^\circ\\\Rightarrow (5x-23)+90+3x+11+90=360\\\Rightarrow 8x-12+180=360\\\Rightarrow 8x-12=360-180\\\Rightarrow 8x=180+12\\\Rightarrow x=24^\circ$

$m\angle EFG=(3x+11)^\circ\\\Rightarrow m\angle EFG=(3\times 24+11)^\circ = 83^\circ$

$m\angle GCE=(5x-23)^\circ\\\Rightarrow m\angle GCE=(5\times 24-23)^\circ\\\Rightarrow m\angle GCE=120-23^\circ\\\Rightarrow m\angle GCE=97^\circ$

So, correct answer is 4th option

$m\angle EFG=83^\circ$ , $m\angle GCE=97^\circ$

Answer from: Quest

answer:

payment just for service

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payment for service including tax

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explanation:

service only with 20% tip

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however, the intention of the question provider may have been that your answer is to be

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payment just for service

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tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

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Study the diagram of circle C. A circumscribed angle, ∠EFG, is tangent to ⨀C at points E and G, and...

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