Question

determine the measure of the unknown angle in each figure.
a.

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

Explanation:

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

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( (n - 2) \times 180^\circ \). This figure is a heptagon (7 sides), so \( n = 7 \). The sum of interior angles is \( (7 - 2) \times 180^\circ = 5 \times 180^\circ = 900^\circ \).

Step2: Sum the known angles.

Add the given angles: \( 139^\circ + 140^\circ + 144^\circ + 127^\circ + 132^\circ + 121^\circ \).
Calculating step by step:
\( 139 + 140 = 279 \)
\( 279 + 144 = 423 \)
\( 423 + 127 = 550 \)
\( 550 + 132 = 682 \)
\( 682 + 121 = 803 \)

Step3: Solve for \( x \).

Subtract the sum of known angles from the total sum of interior angles: \( x = 900 - 803 = 97 \).

Answer:

97