Answer:
5.29
Step-by-step explanation:
Pythagorean theorem is used
We will call AB x
x^2 + 6^2 = 8^2
x^2 + 36 = 64
x^2 = 28
x = 5.2915026
<u>x = 5.26</u>
Answer:
The perimeter of the base of the birdhouse is 36 units
Step-by-step explanation:
<u><em>The complete question is</em></u>
Chase is building a birdhouse in the shape of a regular polygon. He knows that the measure of the interior angle is twice the measure of the exterior angle and the length of a diagonal that passes through the center is 12. What is the perimeter of the base of the birdhouse?
step 1
Find the measure of the interior angle
Let
x ---> the measure of the interior angle
y ---> the measure of the exterior angle
Remember that
the sum of the interior and exterior angle in any polygon is equal to 180 degrees
so
----> equation A
we have that
the measure of the interior angle is twice the measure of the exterior angle
so
----> equation B
substitute equation B in equation A


so

That means-----> The figure is a regular hexagon
step 2
Remember that
The length of the diagonal that passes through the center of the hexagon is equal to two times the length of the regular hexagon
Let
b ----> the length side of the hexagon
so

The perimeter of the hexagon is given by the formula

substitute

Answer:
114 degrees
Step-by-step explanation:
The formula to find the measure of all angles in a regular polygon is
, where n = total number of sides.
Thus, we substitute n for 10, and you get:

If the shape is a regular polygon and it has ten sides, meaning all sides are equal, then all you do is divide 1440 by 10, to get the final answer of 114.
A central angle in a regular ten-sided polygon would be 144 degrees.
You only need two separate ordered pairs for the slope formula
Answer:
5/11
Step-by-step explanation:
4/11 × 10/8
= 40/88
= 5/11