## 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 an

Question

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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3 weeks 2021-09-26T00:05:44+00:00 2 Answers 0

1. 119 degrees is the answer

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°