Given: arc ip + arc vk = 86°
find: ∠ksp

Check the picture below.

using the intersecting chords theorem, let's see, we know that ∡IOP is 43° and since the angle across the junction is a vertical angle, is its twin.

let's recall that a circle has a total of 360°, so if we subtract those two vertical angles, namely 360 - 43 - 43 = 274°.

so the remaining two angles, which are also vertical angles, and therefore twins as well, each one will take 274 ÷ 2 = 137°.

The measure of angle KSP is

Step-by-step explanation:

step 1

Find the measure of angle ISP

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

we have

substitute

step 2

Find the measure of angle KSP

we know that

----> by supplementary angles

we have

substitute

faster, im not sure why but i know it is faster