o is the center of the regular pentagon ABCDE. How many degrees are there in OAB?
Please explain or show work
A.36
B.54
C.72
D.108
E.126
divide 360 into 5 equal parts. What do you get? 72.
But, that is angle AOB, the vertex of an isosceles triangle. So, each of the base angles (OAB and OBA) is (180-72)/2 = 54.
54
Correct! The answer is B. 54 degrees.
To find the number of degrees in angle OAB of a regular pentagon, we need to know the formula for finding the measure of each interior angle of a regular pentagon.
A regular pentagon has five equal sides and five equal angles. To find the measure of each interior angle of a regular pentagon, we can use the formula:
Interior angle measure = (n-2) * 180 / n
Where n represents the number of sides of the polygon.
For a regular pentagon, n = 5, so the formula becomes:
Interior angle measure = (5-2) * 180 / 5
= 3 * 180 / 5
= 540 / 5
= 108
Therefore, each interior angle of a regular pentagon measures 108 degrees.
Since angle OAB is an interior angle of a regular pentagon, it also measures 108 degrees.
Therefore, the answer is option D. 108 degrees.