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Alex787 [66]
3 years ago
6

What set of reflections would carry triangle ABC onto itself?

Mathematics
1 answer:
Neporo4naja [7]3 years ago
6 0

"y-axis, x-axis, y-axis, x-axis" is the one set of reflections among the choices given in the question that <span>would carry triangle ABC onto itself. The correct option among all the options that are given in the question is the fourth option or option "4". I hope that the answer has actually come to your help.</span>
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9514 1404 393

Answer:

  ∠Q = 89°

  ∠R = 123°

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Step-by-step explanation:

It seems easiest to start by finding the measures of each of the arcs. The measure of an arc is double the measure of the inscribed angle it subtends.

  arc QRS = 2·∠P = 114°

So, ...

  arc QR = arc QRS - arc RS = 114° -41° = 73°

The total of the arcs around the circle is 360°, so ...

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  ∠Q = (1/2)(arc RS + arc PS) = (1/2)(41° +137°)

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  ∠R = (1/2)(arc PS +arc PQ) = (1/2)(137° +109°)

  ∠R = 123°

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  ∠S = (1/2)(arc PQ +arc QR) = (1/2)(109° +73°)

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