how many sides does an equiangular polygon have if an angle measures 174?

Answer 1

If you join each "corner" of the unknown polygon to the centre, you draw an unknown number of congruent triangles inside the polygon.

Each of these triangles has 1/2 of 174 degrees for each of it's base angles.

Therefore, the third angle of each triangle = 6 degrees.

You need enough triangles for the total of these 6 degree angles to make up 360 degrees .....("the angle at the centre of a circle = 360 degrees")

6 into 360 = 60

There are 60 triangles inside the polygon

Hence there are 60 triangle bases, which make up the sides of the polygon

The polygon has 60 sides! (You can guess that it will be a huge nimber, because the internal angles of the polygon are 174 degrees, nearly a straight line.)

Answer 2

There are two that come to mind immediately. One is a simple equiangular triangle, the other is a hexacontagon which has 60 sides. [Process: Since an equilateral polygon can be inscribed by a circle, if the angles are 174 degrees then the center angle must be 6 degrees. There are 360 degrees in a circle and simple division yields the answer that you will have 60 vertexes in the center and therefor 60 corresponding sides.
Also, almost true would be a rhombus or a tetragon.

Answer 3

There is a pattern that you can use to help you solve this.
The sum of the angles of a triangle is 180 deg.
If you draw a dot in the middle of a 4-sided polygon, and then draw straight line segments from this dot to each corner of the polygon, you have decomposed the polygon into 4 triangles. The sum of all the angles in these triangles is 4 * 180 deg = 720 deg. The angles around the dot are ones we created; we don't want them. They form a full circle, so they add up to 360 deg.

The remaining angles together comprise the angles of the polygon. Whatever's left after we remove the 360 deg is the sum of their angles. So a 4 sided polygon's angles add to 720 deg - 360 deg = 360 deg.

This same procedure shows that
Angles of 5-sided polygon sum to 540 deg
Angles of 6-sided polygon sum to 720 deg
Angles of 7-sided polygon sum to 900 deg

...each time it's 180 deg more.

To solve your problem (which I won't finish for you), write down the formula for the sum of the angles of an n-sided polygon, in terms of n. Now notice that for an equiangular n-sided polygon, this should just be 174 deg times n. Now you have two different formulas for the same thing; set the two formulas equal to each other, and solve for n.

Answer 4

enable TS = entire style of factors interior the polygon enable TD = entire style of levels interior the polygon enable A = the perspective interior the polygon For any polygon (i.e. extra advantageous than 2 factors), the style of levels interior the polygon is defined as TD = one hundred eighty * (TS - 2) (a triangle has 3 factors and one hundred eighty entire levels, a rectangle has 4 factors and 360 entire levels, and so on.) For any time-honored polygon, all of us understand that the indoors perspective is comparable to the full levels divided by potential of the style of factors: A = TD/TS multiplying the two factors by potential of TS, we get A * TS = TD yet from the 1st equation, all of us understand that TD = one hundred eighty * (TS - 2) so set them equivalent to one yet another: A * TS = one hundred eighty * (TS - 2) all of us understand that A = 174, so substituting and multiplying, we get 174 * TS = (one hundred eighty * TS) - 360 or 360 = 6 * TS or 360/6 = TS or 60 = TS So for a time-honored polygon with inner angles of 174, all of us comprehend it has 60 factors. QED.

Answer 5

You can calculate it based on the exterior angle sum = 360. Since each exterior angle is 6 degrees, you have

360/6 = 60 sides

Answer 6

60