Question

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what is the value of x?
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Explanation:

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

The sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). Here \(n=7\), so the sum \(S=(7 - 2)\times180^{\circ}=900^{\circ}\).

Step2: Set up an equation for the sum of angles

We know that \(146^{\circ}+122^{\circ}+142^{\circ}+140^{\circ}+110^{\circ}+142^{\circ}+x = 900^{\circ}\).
First, calculate the sum of the known angles: \(146 + 122+142+140+110+142=(146+122)+(142+142)+(140 + 110)=268+284+250 = 802^{\circ}\).
Then, solve for \(x\): \(x=900 - 802\).

Answer:

\(98\)