Peter has a set of polygonal tiles, where all the polygons are regular and have the same side length. He find that two pentagons and a decagon can fit together perfectly. Peter also find that a triangle, an octagon, and an n-gon also fit together perfectly. Find n. (Remember that all the tiles are regular polygons.)

24 sides

Step-by-step explanation:

Angle at a point = 360°

To find the number of degrees in each interior angle of a regular polygon, we make use of

180(n - 2)/n

There are 8 sides in a regular octagon,

Each interior of a regular octagon= 180(8-2)/8

= 6 * 180/8

= ¾ * 180

= 135°

The interior angle of a regular triangle (equilateral triangle) is 60°

The interior angle of the regular n-gon is given by

360° - 135 - 60°

= 165°

Since the interior angle is 165°

Then

180(n - 2)/n = 165 for the regular n-gon

Solving for n

Multiply both sides by n

180(n - 2) = 165n Open the bracket

180n - 360 = 165n Collect Like Terms

180n - 165n = 360

15n = 360 Divide both sides by 15

n = 360/15

n = 24

Thus, the number of sides of the regular n-gon is 24

true

step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!