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3 years ago

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

Mathematics

2 answers:

mixer [17]3 years ago

8 0

Answer:

The answer is 40°

Step-by-step explanation:

Solution

Now,

The Measure of major arc FD = 280°

Thus,

One complete angle measure 360°

Then

m∠FED = 360 - 180

m∠FED = 80°

Thus,

FE = DE ( the same circle Radius)

∠EFD = ∠EDF ( opposite angles to equal sides are equal)

Now

Applying angle sum property of a triangle in ΔEFD

∠EFD + ∠EDF + ∠FED = 180°

∠EFD + ∠EFD + 80 = 180

2∠EFD = 100

∠EFD = 50°

Hence, 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 measure of the angle GFD is 40°

MAXImum [283]3 years ago

5 0

Answer:

Step-by-step explanation:

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