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?

Correct answer is 4th option

,

Step-by-step explanation:

Given:

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

, and

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 with the tangent itself.

i.e. ( 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

So, correct answer is 4th option

,

step-by-step explanation:

it's 15

55

step-by-step explanation: