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------------------------------------------------ if the measure of arc CDE=118 degrees and the measure of arc EF=62 degrees calculate measure of angle FGE

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Answer :

The measure of angle FGE from the given figure is 28°.

Given that, the measure of arc CDE = 118° and the measure of arc EF = 62°.

How the measure of an arc and measure of an angle are related?

The measure of an arc is equal to the measure of its corresponding central angle.

From the given figure, the measure of arc CDE = 118° = corresponding central angle (∠CAE)

So, ∠CAE = 118°

From the given figure, the measure of arc FE = 62° = corresponding central angle (∠FAE)

So, ∠FAE = 62°

As we know the radius of a circle is perpendicular to the tangent.

That is, AE ⊥ EG

So, ∠AEG = 90°

Now, ∠AGE+∠AEG+∠GAE = 180° (The sum of interior angles of a triangle is equal to 180°)

∠AGE + 90° + 62° = 180°

⇒ ∠AGE + 152° = 180°

⇒ ∠AGE = 28°

So, ∠AGE = ∠FGE = 28°

Therefore, the measure of angle FGE from the given figure is 28°.

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https://brainly.com/question/16403495.

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The angle FGE will be equal to 28 degrees.

What is an angle of chord theorem?

The phrase "the intersecting chords theorem" refers to a relationship between the four-line segments formed by two intersecting chords inside of a circle. The products of the line segment lengths on each chord, according to this statement, are equal.

Given that if the measure of arc CDE=118 degrees and the measure of arc EF=62 degrees. The angle FGE will be calculated as:-

Angle CDE=118 then the angle AFE will be:-

AFE = 180 - 118 = 62

From the angle of chord theorem angle EBF = 31. Now the angle AFE and AEF will be 59 degrees. Angle GEF will be 31 degrees and angle EFG will be 121 degrees by supplementary property.

Angle EGF = 180 - 121 - 31 = 28

Therefore, the angle FGE will be equal to 28 degrees.

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