Exterior Angles of Polygons

The video tutorial covers the concept of exterior angles in polygons, emphasizing that their sum is always 360 degrees, regardless of the number of sides. It provides step-by-step solutions to problems 22 through 28 from a textbook, demonstrating how to calculate unknown exterior angles using equations and geometric principles. The tutorial also explains the use of parallel lines and transversals in solving these problems.

What is the sum of the exterior angles of any polygon?

• 180 degrees

• 360 degrees

• 540 degrees

• 720 degrees

If a polygon has three exterior angles measuring 140, 110, and x degrees, what is the value of x?

• 130 degrees

• 120 degrees

• 110 degrees

• 100 degrees

In a polygon with four exterior angles, if three angles are 85, 93, and 107 degrees, what is the measure of the fourth angle?

• 95 degrees

• 65 degrees

• 85 degrees

• 75 degrees

For a polygon with five exterior angles, if two angles are represented as z and the others are 45, 55, and 78 degrees, what is the value of z?

• 50 degrees

• 54 degrees

• 58 degrees

• 62 degrees

In a polygon with five exterior angles, if one angle is z + 45 and z is 54, what is the measure of this angle?

• 104 degrees

• 99 degrees

• 95 degrees

• 90 degrees

If a polygon has six exterior angles, and four of them are equal to 45 degrees, what are the measures of the remaining two angles?

• 90 degrees each

• 60 degrees each

• 75 degrees each

• 45 degrees each

In a polygon with parallel lines and transversals, if one interior angle is 125 degrees, what is the measure of the consecutive interior angle?

• 55 degrees

• 45 degrees

• 65 degrees

• 75 degrees

What is the measure of an exterior angle if the corresponding interior angle is 55 degrees?

• 155 degrees

• 145 degrees

• 135 degrees

• 125 degrees

In a polygon with parallel lines, if two alternate interior angles are 55 degrees each, what is the measure of the corresponding exterior angle?

• 145 degrees

• 125 degrees

• 135 degrees

• 115 degrees

If a polygon has exterior angles of 125, 125, 55, and 55 degrees, what is the sum of these angles?

• 300 degrees

• 420 degrees

• 240 degrees

• 360 degrees