Question

Points E, F, and D are on circle C, and angle G

Answer 1

Answer:

The correct statements are:

1: mEFD = mEGD

3: mED = mFD

5: mFD = 120°

Step-by-step explanation:

Let's analyse each statement:

1: mEFD = mEGD

Let's find the value of the angle ECD, using the sum of the internal angles of a quadrilateral:

$60 + 90 + 90 + mECD = 360$

$mECD = 120\°$

The angle ECD is a central angle, related to the arc ED, so the arc ED also has 120°.

The angle EFD inscribes the arc ED, so we have:

$mEFD = mED/2$

$mEFD = 120/2 = 60\°$

So the angles mEFD and mEGD are equal. The statement is TRUE.

2. mEGD = mECD

This statement is FALSE, because mEGD = 60° and mECD = 120°

3. mED = mFD

If mED is 120° and mEF = mFD, we have:

$mED + mEF + mFD = 360$

$2*mFD = 360 - 120$

$mFD = 120\°$

So the statement is TRUE, both arcs have 120°.

4. mEF = 60°

This statement is FALSE, because we calculated before that mEF = mFD = 120°

5. mFD = 120°

This statemente is TRUE, because we calculated before that mFD = 120°.

So the correct statements are 1, 3 and 5