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9 January, 18:49

The measure of an angle is three more than twice its supplement. What is the measure of the angle?

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  1. 9 January, 19:09
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    Answer: the angle is 1°+n*120°

    1°, 121°, 241°

    Step-by-step explanation:

    Angles are taken modulo 360°, so 363° = 3°.

    Angle plus supplement gives 180°.

    Let a be angle, s be supplement of a.

    So s = 180-a. Given a = 3 + 2s

    a = 3 + 2 (180 - a)

    a = 3 + 360 - 2a = 363 - 2a

    3a = 363° or 3° or 723°

    a = 121° or 1° or 241°

    a = 1°

    s = 179°

    2s = 358°

    2s+3 = 361° = 1° (modulo 360)

    a = 121°

    s = 180-121 = 59°

    2s = 118°

    2s + 3 = 121°, as required.

    a = 241°

    s = 360+180-241 = 540-241 = 299

    2s = 598

    2s + 3 = 601 = 241 (modulo 360)
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