Interior Angles Word Problems
To help you see what the sum of all exterior angles of a polygon is, we will use a square and then a pentagon. Since it is very easy to see what the sum is for a square, we will start with the square.
Let us look at the next problem on 'Sum of interior angles of a polygon'. Complementary and supplementary word problems worksheet Area. Sum of Interior Angles of a Polygon. The sum of its angles will be 180° × 3 = 540° The sum of interior angles in a pentagon is 540°. A hexagon (six-sided polygon) can be divided into four triangles. The sum of its angles will be 180° × 4 = 720° The sum of interior angles in a hexagon is 720°.
Notice that an exterior angle is formed by a side of the square and an extension of an adjacent side. For example, x, y, z, and w are exterior angles.
Each interior angle in a square is equal to 90 degrees. Notice that an interior angle plus the adjacent exterior angle is equal to 180 degrees.
Interior angle + adjacent exterior angle = 180 degrees.
For example, 90 + w = 180 degrees
w = 90 degrees
Since there are 4 exterior angles, 4 x 90 = 360 degrees.
To find the measure of the interior angle of a pentagon, we just need to use this formula.
[(n - 2 ) 180] / n
Since n is equal to 5, [(n - 2 ) 180] / n = [(5 - 2) 180] / 5 = [3 x 180] / 5 = 540 / 5 = 108
Again, Interior angle + adjacent exterior angle = 180 degrees.
108 + adjacent exterior angle = 180 degrees
adjacent exterior angle = 180 - 108 = 72
Since there are 5 exterior angles, 5 x 72 = 360 degrees.
It does not matter how many sides the polygon has, the sum of all exterior angles of a polygon is always equal to 360 degrees.
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In geometry, you can find the sum of the interior or exterior angles of a polygon based on the number of sides the polygon has. You can then apply this information to find individual interior or exterior angles.
The sum of the exterior angles of any polygon is 360 degrees. The formula
tells you the sum of the interior angles of a polygon, where n represents the number of sides.
Practice questions
Use your knowledge of the sums of the interior and exterior angles of a polygon to answer the following questions.
Solve for x.
Solve for x.
Answers and explanations
58 degrees
The sum of the exterior angles of a polygon is 180 (n – 2), where n represents the number of sides. The sum of the angles of a pentagon (five sides) is equal to
The pentagon is missing one interior angle, which you can call y:
The interior and exterior angles of a polygon are supplementary. Therefore,
20 degrees
The sum of the interior angles of a polygon is 180 (n – 2), where n represents the number of sides. The sum of the angles of a hexagon (six sides) is equal to
Add the interior angles, set the sum equal to 720, and solve for x: