Question

what is the greatest angle measure in the diagram? (15x - 10)° (15x + 14)° (11x + 10)° (9x - 4)° 96° 105° 119° 180°

Explanation:

1. First, use the property that the sum of the interior - angles of a quadrilateral is \(360^{\circ}\):

• \((15x - 10)+(15x + 14)+(11x + 10)+(9x - 4)=360\).
• Combine like - terms: \((15x+15x + 11x+9x)+(-10 + 14+10 - 4)=360\).
• \(50x + 10 = 360\).
• Subtract 10 from both sides: \(50x=360 - 10=350\).
• Divide both sides by 50: \(x = 7\).

1. Then, find the measure of each angle:

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

1. Compare the angle measures:

• The angle measures are \(95^{\circ}\), \(119^{\circ}\), \(87^{\circ}\), and \(59^{\circ}\).
• The greatest angle measure is \(119^{\circ}\).

Answer:

\(119^{\circ}\)