Question

What fractional part of one semicircle does the labeled angle represent? Express your answer as a fraction in simplest terms. Then, express the labeled angle in radian measure.Please fill in the two blanks as fractions (if needed)

Answer 1

Remember that

A complete circle has 360 degrees

A semicircle has 180 degrees

so

Applying proportion

100/180=x/225

solve for x

x=(100/180)*225

x=22,500/180

x=125%

Convert to fraction

125/100

simplify

5/4

therefore

the labeled angle represents 5/4

Part b

Express the labeled angle in radian measure

Remember that

pi radian -------> represents 180 degrees

so

225 degrees

radians=225pi/180

5pi/4