Question

1. five angles of a hexagon measure (119^circ), (129^circ), (104^circ), (139^circ), and (95^circ). what is the measure of the sixth angle?

Explanation:

Step1: Recall the sum of interior angles of a hexagon

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a hexagon, \(n = 6\), so the sum is \((6 - 2)\times180^{\circ}=4\times180^{\circ} = 720^{\circ}\).

Step2: Calculate the sum of the five given angles

Add the five angles: \(119^{\circ}+ 129^{\circ}+104^{\circ}+139^{\circ}+95^{\circ}\).
First, \(119 + 129 = 248\); \(248+104 = 352\); \(352 + 139 = 491\); \(491+95 = 586^{\circ}\).

Step3: Find the sixth angle

Subtract the sum of the five angles from the total sum of interior angles of the hexagon. Let the sixth angle be \(x\), then \(x=720^{\circ}- 586^{\circ}=134^{\circ}\).

Answer:

The measure of the sixth angle is \(134^{\circ}\).