Respuesta :

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°.

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calculista

Answer:

The measure of angle KSP is [tex]137\°[/tex]

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.

[tex]m<ISP=\frac{1}{2}(arc\ VK+arc\ IP)[/tex]

we have

[tex](arc\ VK+arc\ IP)=86\°[/tex]

substitute

[tex]m<ISP=\frac{1}{2}(86\°)=43\°[/tex]

step 2

Find the measure of angle KSP

we know that

[tex]m<ISP+m<KSP=180\°[/tex] ----> by supplementary angles

we have

[tex]m<ISP=43\°[/tex]

substitute

[tex]43\°+m<KSP=180\°[/tex]

[tex]m<KSP=180\°-43\°=137\°[/tex]

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