Question

What is the measure of each interior angle of a regular 14-gon

Answer 1

Hello!

The answers are:

Question 7:

154.29°

Question 8:

Yes, because the opposite sides are congruent.

Why?

For question 7:

We know that the sum of all interior angles of any polygon is determined by the following formula:

$Angles=180*(sides-2)$

Therefore the sum of all interior angles of a 14-gon is equal to 2160°, so, the measure of each interior angle is given by the following calculation:

$14-gon=(14-2)*180\°=2160\°$

Each interior angle is equal to:

$\frac{2160\°}{12}=154.29\°$

For question 8:

We know that a quadrilateral is a parallelogram when the opposite sides are parallel or congruent.

From the statement we know that:

BE≅ED

and

AE≅EC

So, we can assume that the triangles formed by the sides BE and AE, and the sides EC and ED, are also congruent, meaning that the opposite sides BA and CD are congruent, so, the quadrilateral is a parallelogram.

Have a nice day!