Question

find the missing angle measure.
the measure of the missing angle is \\(\square^{\circ}\\).
(type an integer or a fraction.)

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon. For an n - sided polygon, the sum of interior angles is \((n - 2)\times180^{\circ}\). Here, the figure is a hexagon (\(n = 6\)), so the sum of interior angles is \((6 - 2)\times180^{\circ}=720^{\circ}\).

Step2: Sum up the given angles. The given angles are \(142^{\circ}\), \(165^{\circ}\), \(60^{\circ}\), \(130^{\circ}\), \(127^{\circ}\). Their sum is \(142 + 165+60 + 130+127\) \(=142+165 = 307\); \(307+60 = 367\); \(367+130 = 497\); \(497+127 = 624^{\circ}\).

Step3: Let the missing angle be \(x\). Then, using the sum of interior angles of a hexagon, we have \(x+624 = 720\). Solving for \(x\), we get \(x=720 - 624=96^{\circ}\).

Answer:

\(96\)