Question

3 In the figure, point us in the interior
of The circle then find m (arc PR).
using theorem . Remote agIes. Find the
measure of SPQ and hence
Find m (arc sQ)
​

Answer 1

Answer:

m(arc PR) = 80°

 the measure of angle SPQ = 60°

  m (arc SQ) = 120°

Step-by-step explanation:

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°  = 60°

m (arc SQ)

∠ SPQ = 1/2 * m(arc SQ)

60° = 1/2 * m(arc SQ)

m(arc SQ) = 120°

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HOPE IT HELPS!!!!

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