Question

what is the greatest angle measure in the diagram? 95° 105° 119° 180°

Explanation:

Step1: Use the sum of interior angles formula for a quadrilateral

The sum of interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\). So, \((15x - 10)+(15x + 14)+(11x + 10)+(9x - 4)=360\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((15x+15x + 11x+9x)+(-10 + 14+10 - 4)=360\).
\(50x + 10=360\).

Step3: Solve for \(x\)

Subtract 10 from both sides: \(50x=360 - 10=350\).
Divide both sides by 50: \(x=\frac{350}{50}=7\).

Step4: Calculate each angle measure

• For \(\angle E=(15x - 10)^{\circ}\), substitute \(x = 7\): \((15\times7-10)^{\circ}=(105 - 10)^{\circ}=95^{\circ}\).
• For \(\angle F=(15x + 14)^{\circ}\), substitute \(x = 7\): \((15\times7+14)^{\circ}=(105 + 14)^{\circ}=119^{\circ}\).
• For \(\angle H=(11x + 10)^{\circ}\), substitute \(x = 7\): \((11\times7+10)^{\circ}=(77 + 10)^{\circ}=87^{\circ}\).
• For \(\angle G=(9x - 4)^{\circ}\), substitute \(x = 7\): \((9\times7-4)^{\circ}=(63 - 4)^{\circ}=59^{\circ}\).

Answer:

\(119^{\circ}\)