Based on the inscribed angle theorem, the measure of arc ECF in circle (G) is equal to: B. 98 degrees.
What is the inscribed angle theorem?
The inscribed angle theorem states that the measure of an inscribed angle whose vertex lies on a circle is half of the intercepted arc subtended at a point on the circle.
Given the following data:
By using the inscribed angle theorem, we would find the intercepted arc as follows:
∠DEF = ∡DF/2
79 = ∡DF/2
∡DF = 2 × 79
∡DF = 158 degrees.
Now, we can determine measure of arc ECF:
∡ECF + ∡DF + ∡DE = 360
∡ECF + 158 + 104 = 360
∡ECF + 262 = 360
∡ECF = 360 - 262
∡ECF = 98 degrees.
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