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Line t is tangent to the circle. Find the measure of arc DEF.

The measure of arc DEF is (blank)

What is the degree measurement of arc DEF? Please show all the work on how you got your answer. (Note: You do not have to explain your work if you can't. All I am asking for is the work shown with your answer)

  234°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the arc it intercepts. That is the same as saying the measure of the arc is twice the measure of the inscribed angle intercepting it.

An inscribed angle is generally defined by 3 points on the circle: two at the ends of the arc, and one at the vertex of the angle. As the vertex of the angle gets closer to one of the ends of the arc, the chord between the two points (vertex and arc end) becomes closer and closer to a tangent to the circle.

The relationship between the angle measure and the arc measure remains true, even when the angle is between a tangent (line t) and the chord to the other end of the arc (segment DF). That is, the intercepted arc is twice the angle measure:

  Arc DEF = 2 × ∠D = 2 × 117° = 234°

234°

Step-by-step explanation:

Consider the isosceles triangle formed by the centre and FD

Angle at the centre:

180 - 2(117 - 90)

126

Required angle:

360 - 126

234

answer: an 8-foot rope is tied from the top of a pole to a

stake in the ground, as shown in the diagram

below

step-by-step explanation: