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lyudmila [28]
2 years ago
9

Angles A = 60, B = 2x, C = 3x and D = 25 are 4 angles on a straight, what 3 points is the value of angle B?*​

Mathematics
1 answer:
iragen [17]2 years ago
4 0

Answer:

  B = 38°

Step-by-step explanation:

A straight angle is 180°. If your four angles total a straight angle, then ...

  60 +2x +3x +25 = 180

  95 = 5x . . . . . . subtract 85

  x = 19 . . . . . . divide by 5

  2x = 38 . . . . . angle B is 38°

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(1) Recall the angle sum identity for cosine:

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cos(<em>π</em>/3) cos(5<em>π</em>/6) - sin(<em>π</em>/3) sin(5<em>π</em>/6) = cos(<em>π</em>/3 + 5<em>π</em>/6)

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(2) Recall the half-angle identity:

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Since <em>π</em>/2 < 7<em>π</em>/12 < <em>π</em>, you should expect cos(7<em>π</em>/12) < 0. So solving for cos(<em>x</em>) above, we have

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Then

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(tan(122°) - tan(32°))/(1 + tan(122°) tan(32°)) = tan(122° - 32°)

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(4) Recall the double angle identity for sine:

sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)

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Consult the other question you commented on [19739123 in the URL] for details on (7) and (8).

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Answer:

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Step-by-step explanation:

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