Acentral angle θ in a circle of radius 4 m is subtended by an arc of length 5 m. find the measure of θ in degrees. (round your answer to one decimal place.)

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

we have

substitute the values

step 2

Remember that

360 degrees subtends the arc of length   (circumference)

so

by proportion

Find the measure of θ by an arc of length 5 m

assume

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq