In fig. point T lies in the interior of the circle then find a) m(arc PR)b) using theorem of remote interior angle, find the measure of angle SPQ and hence find m(arcSQ)c) Relate measure of angle STQ with m(arcPR) and m(arcSQ)
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Explained in the pic... please refer
third sub question is very easy just refer to pic above....
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In fig. point T lies in the interior of the circle.
Consider the attached figure while going through the following steps
a) m(arc PR)
we use the formula
∠ = 1/2 * m(arc __)
∠ PSR = 1/2 * m(arc PR)
40° = 1/2 * m(arc PR)
m(arc PR) = 80°
b) ∠ SPQ
Using the theorem of remote interior angles, we have,
the measure of an interior angle is equal to the sum of measures of interior angles.
∠ SPQ +∠ PST = ∠ STQ
∠ SPQ = ∠ STQ - ∠ PST
= 100° - 40°
∴ ∠ SPQ= 60°
m (arc SQ)
∠ SPQ = 1/2 * m(arc SQ)
60° = 1/2 * m(arc SQ)
m(arc SQ) = 120°
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