a To calculate the measure of an interior angle of a regular n-gon, we can use the formula 180^(∘)(n-2)n, where n is the number of sides in the polygon. A pentagon is a polygon with 5 sides.
The sum of the central angles in any regular polygon equals 360^(∘). Since an equilateral triangle has 3 congruent central angles, we can determine the measure of a by dividing 360^(∘) by 3.
360^(∘)/3= 120^(∘)
As we can see, a=120^(∘) and b=108^(∘). Therefore a is greater than b.
From our calculations we see that b is greater than a.
d The equation tells us that to obtain a we have to add 3 to b. This must mean that a is greater than b.
a = b + 3
a is 3 greater than b
e Like in Part A, we can use trigonometric ratios to write equations containing a and b. For the triangle on the left we need to use the tangent ratio. In the triangle on the right, we need to use the cosine ratio.
