If ray NP bisects

Question

If ray NP bisects <MNQ, m<MNQ=(8x+12)°, m<PNQ=78°, and m<RNM=(3y-9)°, find the value of x and y

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Answers ( No )

    0
    2021-11-23T23:23:29+00:00

    Step 1

    Find the measure of angle x

    we know that

    If ray NP bisects <MNQ

    then

    m<MNQ=m<PNM+m<PNQ ——> equation A

    and

    m<PNM=m<PNQ ——-> equation B

    we have that

    m<MNQ=(8x+12)°

    m<PNQ=78°

    so

    substitute in equation A

    (8x+12)=78+78——-> 8x+12=156——> 8x=156-12

    8x=144——> x=18°

    Step 2

    Find the measure of angle y

    we have

    m<PNM=(3y-9)°

    m<PNM=78°

    so

    3y-9=78——> 3y=87——> y=29°

    therefore

    the answer is

    the measure of x is 18° and the measure of y is 29°

    0
    2021-11-23T23:23:43+00:00

    Answer: If NP bisects MNQ, MNQ=8x+12,PNQ=78, and RNM=3y-9, find the values of x and y

    x= 18 y=11

    Step-by-step explanation:

    We know that MNQ= 8x+12

    PNQ=78 and MNP is equal to PNQ

    Therefore, PNQ=MNP

    So since these two angles make up MNQ,

    Add 78+78 which is 156

    So now we need to find x

    The equation to find x is 8x+12=156

    8x+12=156

    8x=144

    x=18

    Now that we know x it is time to find y.

    So we know that RNM=3y-9

    And we know that MNQ is equal to 156

    RNM an MNQ form a straight line which means that it is equal to 180 degrees

    So the equation to find y is 3y-9+156=180

    3y-9+156=180

    3y+147=180

    3y=33

    y=11

    So in conclusion, x=18 and y=11

    Hope this helped! :3

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