Question

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

Explanation:

Step1: Determine the number of sides (n)

The figure is a hexagon, so \( n = 6 \).

Step2: Calculate the sum of interior angles

The formula for the sum of interior angles of a polygon is \( (n - 2) \times 180^\circ \). For \( n = 6 \), we have:
\[
(6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
\]

Step3: Sum the known angles

The known angles are \( 144^\circ \), \( 164^\circ \), \( 56^\circ \), \( 135^\circ \), and \( 120^\circ \). Let's sum them:
\[
144 + 164 + 56 + 135 + 120 = 619^\circ
\]

Step4: Find the missing angle (x)

Subtract the sum of the known angles from the total sum of interior angles:
\[
x = 720 - 619 = 101^\circ
\]

Answer:

\( 101 \)