Question

b.

enter the answer in the space provided. use numbers instead of words.

$x^{\circ}=\square^{\circ}$

Explanation:

Step1: Find sum of interior angles of pentagon

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 pentagon, \(n = 5\), so the sum is \((5 - 2)\times180^\circ= 540^\circ\).

Step2: Calculate the unknown interior angle

Let the unknown interior angle (adjacent to \(x^\circ\)) be \(y^\circ\). We know four interior angles: \(120^\circ\), \(90^\circ\), \(108^\circ\), \(100^\circ\). So \(120 + 90 + 108 + 100 + y = 540\).
Simplify: \(418 + y = 540\), so \(y = 540 - 418 = 122^\circ\).

Step3: Find \(x\) using linear pair

Since \(y\) and \(x\) form a linear pair, \(y + x = 180\). So \(122 + x = 180\), so \(x = 180 - 122 = 58\).

Answer:

58