Answer:
(a) mFG = 108°
(b) m∠FEG = 108°
Step-by-step explanation:
Since FH is tangent to the circle, the angle EFG can be calculated as follows:
∠EFG + ∠GFH = 90°
So, replacing the measure of ∠GFH, we can calculate ∠EFG as:
∠EFG + 54° = 90°
∠EFG = 90° - 54°
∠EFG = 36°
Now, the triangle formed by points E, G, and F is isosceles because the length of EF is equal to the length of EG. It means that the ∠EFG has the same measure as ∠EGF, so we can calculate the measure of ∠FEG as:
∠EFG + ∠EGF + ∠FEG = 180°
Because the sum of the interior angles of a triangle is 180°-
So, replacing ∠EFG and ∠EGF by 36°, we get:
36° + 36° + ∠FEG = 180°
72° + ∠FEG = 180°
∠FEG = 180° - 72°
∠FEG = 108°
Therefore, the answers are:
(a) mFG = 108°
(b) m∠FEG = 108°
Because the measure of the arc FG is the same measure of ∠FEG.