Question

A wooden plate is shaped as a pentagon. The measure of one angle is 40°. The remaining interior angles are obtuse and of equal measure.

What is the measure of each obtuse angle in the pentagon?

Answer 1

So, what is the total of the interior angles of a pentagon?

Answer 2

one of these four. 126°

180°

174°

150

Answer 3

I'm asking what the total is if you summed all the internal angles. I know what the answer to this is, but I'd rather guide you to it than just give it to you. You don't learn anything if I just tell you the answer.

Answer 4

this is the new question you can guide me on. lol A picture frame is shaped as a heptagon. The measure of one angle is 144°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?

Answer 5

Sure it would. This is just something you look up or memorize.

The summation of the internal angles of a polygon equals (n-2)*180, where n is the number of sides of the polygon.

Answer 6

The new equation is pretty much exactly the same, just a different shape.

So, how many sides are on a heptagon?

Answer 7

7

Answer 8

Ok, so the summation of the internal angles is:

(7-2)*180 = 900

Answer 9

We know one angle, and we know the other 6 are all equal. So how would you find them?

Answer 10

divide 900 by 7?

Answer 11

No, we know one angle, so we have to remove that angle first. Subtract 144. The remaining 6 angles are all equal, so we can then divide by 6 to get 6 equal parts.

Answer 12

so it will equal 150

Answer 13

You need to construct a regular polygon. When you draw two sides, the interior angle created between them is 144°, illustrated below.

Angle measuring 144 degrees.

What will be the sum, in degrees, of the measures of the interior angles of this polygon when it is completed?

720°

1080°

1440°

900°

Answer 14

Alright, so the easy way to do this is to realize that a regular polygon can be described by laying a series of identical triangles side by side.

The "outter" two angles of the triangles will each be one half of an interior angle, and the total of the interior angles of a triangle is 180. Thus, the angle of the triangle in the center of the polygon is 180-interior angle of the polygon.

Does this make sense?