Question

Minor arc KL measures 135º

Which is the radian measure of central angle KOL?

o 3T radians

O

31 radians

O

TT radians

13.

radians

Answer 1

`(3 \pi)/(4) \ radians`.

Explanation:

We know that a central angle is equal to its subtended arc.

In this case, the subtended arc is 135°, that means the central angle KOL is equal to 135°.

Then, we transform from degrees to radians. We know that
`\pi` is equivalent to 180°, so we use the rule of three.

`x=135\° * (\pi)/(180\°)= (3 \pi)/(4) \ radians`

Using
`\pi \approx 3.14`, we have

`x \approx 2.36 \ radians`

Therefore, the radian measure of the central angle is
`(3 \pi)/(4) \ radians`.