Question

find the measure of angle x in the figure.

note: angles not drawn to scale.

angle x measures \\(\square^\circ\\)

Explanation:

Step1: Determine the number of sides

The figure is a heptagon (7 - sided polygon). The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For \(n = 7\), the sum is \((7 - 2)\times180^{\circ}=5\times180^{\circ}=900^{\circ}\).

Step2: Sum the known angles

Add the given angles: \(132^{\circ}+122^{\circ}+121^{\circ}+126^{\circ}+139^{\circ}+139^{\circ}\).

$$
LATEXBLOCK0
$$

Step3: Solve for \(x\)

Subtract the sum of known angles from the total sum: \(x = 900^{\circ}-779^{\circ}=121^{\circ}\).

Answer:

\(121\)