Question

in exercises 9–14, find the value of x. (see example 3.)
9.
10.
11.
12.
13.
14.

Explanation:

Problem 9:

Step1: Recall quadrilateral angle sum

A quadrilateral's interior angles sum to \( (4 - 2) \times 180^\circ = 360^\circ \).

Step2: Sum known angles

Known angles: \( 100^\circ, 130^\circ, 66^\circ \). Sum: \( 100 + 130 + 66 = 296^\circ \).

Step3: Solve for \( x \)

\( x = 360 - 296 = 64^\circ \).

Step1: Quadrilateral angle sum

Interior angles of a quadrilateral sum to \( 360^\circ \).

Step2: Sum known angles

Known angles: \( 103^\circ, 133^\circ, 58^\circ \). Sum: \( 103 + 133 + 58 = 294^\circ \).

Step3: Solve for \( x \)

\( x = 360 - 294 = 66^\circ \).

Step1: Quadrilateral angle sum

Quadrilateral angles sum to \( 360^\circ \).

Step2: Sum known angles

Known angles: \( 154^\circ, 88^\circ, 29^\circ \). Sum: \( 154 + 88 + 29 = 271^\circ \).

Step3: Solve for \( x \)

\( x = 360 - 271 = 89^\circ \).

Answer:

\( 64^\circ \)

Problem 10: