What is the length of the missing leg
1 answer:
You might be interested in
Answer:
The polygon has sides.
Step-by-step explanation:
Recall that the expression for finding the measure of one interior angle of a regular polygon is , where
is the number of sides the polygon has (and
), which is what we want to find.
Because the measure of one interior angle of the given polygon is , we can write the following equation to solve for
:
Solving for , we get:
(Distribute the
in the numerator)
(Multiply both sides of the equation by
to eliminate the denominator and simplify)
(Subtract
from both sides of the equation and simplify)
(Add
to both sides of the equation to isolate
and simplify)
(Divide both sides of the equation by
to get rid of
's coefficient and simplify)
Therefore, the polygon has sides. Hope this helps!