Question

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

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon.

For a polygon with \( n \) sides, the sum of interior angles is \( (n - 2)\times180^\circ \). Here, the figure is a hexagon (\( n = 6 \)), so the sum is \( (6 - 2)\times180^\circ = 4\times180^\circ = 720^\circ \).

Step2: Sum the given angles.

The given angles are \( 144^\circ \), \( 164^\circ \), \( 58^\circ \), \( 131^\circ \), \( 120^\circ \), and we need to find \( x^\circ \). Let's sum the known angles: \( 144 + 164 + 58 + 131 + 120 \).
Calculating that: \( 144 + 164 = 308 \); \( 308 + 58 = 366 \); \( 366 + 131 = 497 \); \( 497 + 120 = 617 \).

Step3: Solve for \( x \).

The sum of all interior angles is \( 720^\circ \), so \( x + 617 = 720 \). Subtract \( 617 \) from both sides: \( x = 720 - 617 = 103 \).

Answer:

\( 103 \)