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?

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°