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6 February, 18:47

Quadrilateral E F G H is shown. Angle E is (15 x minus 10) degrees, angle F is (15 x + 14) degrees, angle G is (9 x minus 4) degrees, and angle H is (11 x + 10) degrees.

What is the greatest angle measure in the diagram?

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  1. 6 February, 19:14
    0
    Step-by-step explanation:let's find the value of x first

    The sum of all the angles of a quadrilateral is 360°

    (15x-10) ° + (15x+14) ° + (9x-4) ° + (11x+10) ° = 360°

    Open up the brackets and rearrange the expression

    15x-10°+15x+14°+9x-4°+11x+10°=360°

    15x+15x+9x+11x-10°+14°-4°+10° = 360°

    50x+10°=360°

    Collect like terms

    50x=360°-10°

    50x=350°

    Divide by the coefficient of x

    x = 350/50

    X=7°

    Substitute the value of x into the various angles

    15x-10° = (15*7) - 10 = 105-10=95°

    15x+14° = (15*7) + 14=105+14=119°

    9x-4° = (9*7) - 4=63-4=59°

    11x+10° = (11*7) + 10=77+10=87°

    The greatest angle measure is angle F which is 119°
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