Question

find the value of x. the measure of x is degrees. 90° 120° 108° 100° x°

Explanation:

Step1: Calculate the sum of interior angles of a pentagon

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

Step2: Find the adjacent interior angle of \(x\)

Let the adjacent interior angle of \(x\) be \(y\). We know that \(y+x = 180^{\circ}\) (linear - pair of angles).
The sum of the given interior angles: \(90^{\circ}+120^{\circ}+108^{\circ}+100^{\circ}+y=540^{\circ}\).
Simplify the left - hand side: \(418^{\circ}+y = 540^{\circ}\).
Solve for \(y\): \(y=540^{\circ}-418^{\circ}=122^{\circ}\).

Step3: Calculate the value of \(x\)

Since \(y + x=180^{\circ}\) and \(y = 122^{\circ}\), then \(x=180^{\circ}-y\).
Substitute \(y = 122^{\circ}\) into the equation: \(x=180^{\circ}-122^{\circ}=82^{\circ}\).

Answer:

\( 82 \)