if c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE

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if c is the incenter of AMD, AMC=3x+6 AND dmc = 8X-49, FIND EACH MEASURE

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    0
    2021-09-10T08:01:58+00:00

    Answer:

    m\angle AMC = 39\° and m\angle DMC = 39\°.

    Step-by-step explanation:

    As you can observe in the image attached, angles AMC and DMC are congruent, because if point C is the incenter of AMD, that means each line the forms such point is a bisector.

    Remember that a bisector is a line that equally divides an angle.

    So,

    \angle AMC = \angle DMC\\3x+6=8x-49

    Solving for x, we have

    6+49=8x-3x\\5x=55\\x=11

    Then, we substitute this value in each expression to find the angles.

    \angle AMC = 3x+6 = 3(11)+6=33+6=39

    \angle DMC = 8(11)-49=88-49=39

    Therefore, the measures of those angles are m\angle AMC = 39\° and m\angle DMC = 39\°.

    0
    2021-09-10T08:02:31+00:00

    3x+6=8x-49,
    -6. -6
    __________
    3x=8x-55
    -8x. -8x
    ________
    -5x=-55
    x=11,
    3(11)+6=39
    8(11)-49=39

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