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2. There is an equilateral triangle, ABC, inscribed in a circle with center D. What is the smallest angle you can rotate triangle ABC around D so that the image of A is B?

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waldothewizard

Answer:

120 degrees.

Step-by-step explanation:

All angles in an equilateral triangle measure 60°

All angles subtend arcs of 120°.

B must move through 120° to replace A.

This is about angles in inscribed objects.

Angle is 120°.

  • Equilateral triangles are triangles with three equal sides. This also means that all three internal angles will be equal.

Now, the sum of angles in a triangle is 180°.

Thus, each interior angle of the triangle will measure; 180°/3 =  60°

  • Now, i have attached an image showing an equilateral triangle inscribed in a circle.

  • From the image, we can say that All 3 angle points will subtend an arc with an angle of 120° at the center of the circle. This is because from the exterior angle theorem, the angle subtended by an arc of a circle at the center of that same circle will be double the angle it subtends anywhere on its' circumference which in this case, means 2 × 60 = 120° .

This means that the smallest angle we can rotate around D so that image of A is B is 120°

Read more at; https://brainly.com/question/15539775

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