Question

In the figure,point T lies in the interior of the circle then find:m(arcPR) (b) using theorem of remote interior anglws, find the measure of angle SPQ and hence find m (arcSQ)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

m(arcPR) = 80°

(b) the measure of angle SPQ = 60° and hence  m (arcSQ) = 120°

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°