Question

find the measures of the missing angles (hint: first determine the sum of the interior angles of the polygon).

Explanation:

Step1: Calculate the sum of interior angles for a pentagon

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\). For a pentagon (\(n = 5\)), the sum is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up the equation to find \(n\)

We know the angles \(147^{\circ},145^{\circ},122^{\circ},139^{\circ},141^{\circ},147^{\circ}\) and \(n^{\circ}\). The sum of these angles is \(147 + 145+122 + 139+141+147+n=540\).

$$147+145 + 122+139+141+147+n=540$$

$$841 + n=540$$

$$n=540 - 841$$

$$n = 149^{\circ}$$

Answer:

\(n = 149^{\circ}\)