A convex hexagon has five interior angles measuring 115^\circ, 125^\circ, 130^\circ, 140^\… — GRE General Test

A convex hexagon has five interior angles measuring $115^\circ$ , $125^\circ$ , $130^\circ$ , $140^\circ$ , and $150^\circ$ . What is the measure, in degrees, of the exterior angle adjacent to the sixth interior angle?

A
$60^\circ$
B
$80^\circ$
$120^\circ$ Answer
D
$140^\circ$
E
$150^\circ$

Answer

The measure of the exterior angle adjacent to the sixth interior angle is

120^\circ

The sum of the interior angles of a 6-sided polygon (hexagon) is given by

(6 - 2) \times 180^\circ = 720^\circ

. The sum of the five given interior angles is

115^\circ + 125^\circ + 130^\circ + 140^\circ + 150^\circ = 660^\circ

, which leaves

720^\circ - 660^\circ = 60^\circ

for the sixth interior angle. Since an interior angle and its adjacent exterior angle are supplementary, the exterior angle is

180^\circ - 60^\circ = 120^\circ

Step-by-Step Solution

Calculate the sum of the interior angles for a convex hexagon.

Using

(n - 2) \times 180^\circ

with

n = 6

, the total interior angle sum is

(6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ

The sum of interior angles of any convex polygon with

n

sides is

(n - 2) \times 180^\circ

Find the sum of the five given interior angles.

115^\circ + 125^\circ + 130^\circ + 140^\circ + 150^\circ = 660^\circ

Summing the five known angle values is necessary to find the remaining sixth angle.

Determine the measure of the sixth interior angle.

720^\circ - 660^\circ = 60^\circ

Subtracting the sum of the five interior angles from the total interior angle sum yields the sixth interior angle.

Calculate the supplementary exterior angle.

180^\circ - 60^\circ = 120^\circ

An interior angle and its adjacent exterior angle form a straight line and are supplementary (

180^\circ

Key Concept

Interior and Exterior Angles of Convex Polygons

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