In the figure, if MR = MK

arc RK = 360 - 260 = 100º

∠RMK = 100 / 2 = 50º

∠MKQ = 23 / 2 = 11.5º

∠KPM = 180 - (50 + 11.5) = 118.5º

∠RPK = 1/2 (360 - 118.5 * 2) = 61.5º

In the figure, if MR = MK, the measure of arc MK is 130 degrees, and measure of arc MQ is 23 degrees, then what is angle RPK, in degrees?

Let X be the centre

Mz understanding of the question is that   

and you want 

When two angles stand on the same arc, the angle at the centre is twice the angle on the circumference,

so

None of the other info is relevant.

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For some reason this is not displaying properly, so hee is a picture of it

Test post

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