Angle g is a circumscribed angle of circle e. major arc fd measures 280°. what is the measure of angle gfd? 40° 50° 80° 90°

The correct option is A. 40°

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Measure of major arc FD = 280°

Since, one complete angle measure 360°

⇒ m∠FED = 360 - 180

⇒ m∠FED = 80°

Now, FE = DE ( Radius of the same circle)

⇒ ∠EFD = ∠EDF ( Angles opposite to equal sides are equal)

Now, using angle sum property of a triangle in ΔEFD

⇒ ∠EFD + ∠EDF + ∠FED = 180°

⇒ ∠EFD + ∠EFD + 80 = 180

⇒ 2∠EFD = 100

⇒ ∠EFD = 50°

Now, GF is tangent to the circle and the tangent always make right angles with the radius of the circle.

⇒ ∠EFG = 90°

⇒ ∠GFD + ∠EFD = 90°

⇒ ∠GFD + 50 = 90

⇒ ∠GFD = 40°

Therefore, The correct option is A. 40°

The measure of ∠GFD is 40°

Step-by-step explanation:

Given that angle G is a circumscribed angle of circle E. Major arc FD measures 280°.

we have to find the measure of ∠GFD

As in figure

Measure of major arc FD = 280°

Since, one complete angle measure 360°

⇒ m∠FED = 360 - 180

⇒ m∠FED = 80°

Now, FE = DE ( Radius of the same circle)

⇒ ∠EFD = ∠EDF ( Angles opposite to equal sides are equal)

By angle sum property of a triangle in ΔEFD

⇒ ∠EFD + ∠EDF + ∠FED = 180°

⇒ ∠EFD + ∠EFD + 80 = 180

⇒ 2∠EFD = 100

⇒ ∠EFD = 50°

Now, GF is tangent to the circle and by theorem the tangent always make right angles with the radius of the circle.

⇒ ∠EFG = 90°

⇒ ∠GFD + ∠EFD = 90°

⇒ ∠GFD + 50 = 90

⇒ ∠GFD = 40°

Therefore, the correct option is A.

The measure of ∠GFD is 40°