Central angle of circle P is a angle equals to 121° and 73°.
The measure of arc RU is 59 degrees
" A circle is closed two dimensional shape , whose all points on the surface are equidistant from its center."
Definition of arc measure
"In a circle, the degree measure of an arc is equals to the central angle present in the included arc."
According to the question,
∠TPU and ∠UPR are supplementary angles.
Given , ∠UPR = 59°
Therefore,
∠TPU = 180° - 59°
= 121°
∠TPQ + ∠QPR = 180°
∠QPR = 107°
Therefore ,
∠QPR = 180° - 107°
= 73°
As per the definition of arc measure, we conclude
The measure of arc RU is equals to 59degrees.
Hence, central angle of circle P is a angle equals to 121° and 73° and
measure of arc RU is 59 degrees.
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