In circle O, angle measure of POV and angle measure of SOR are supplementary - if the measure of angle SOR = 3X, the measure of angle POV = 2x+ 80, and the measure of POS = 5x+10, find the measures of each of the following?

Question

a) x
b) measure of angle SOR
c) measure of angle POV
d) measure of angle POS
e) measure of angle VOR
f) measure of arc length SR
g) measure of arc length RV
h) measure of arc length PV
i) measure of arc length PS
J) measure of arc length SPV
k) measure of arc length VSP
l) measure of arc length RPV

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Answer 1 · 2018-05-28T11:31:54

See below.

If #/_POV# and #/_SOR# are supplementary, then:

#/_POV+/_SOR=180^@#

#/_POV=2x+80+3x=180^@=>color(blue)(x=20^@)#

#/_POV=2x+80=2(20)+80=color(blue)(120^@)#

#/_POS=5x+10=5(20)+10=color(blue)(110^@)#

#/_SOR=3x=3(20)=color(blue)(60^@)#

#/_SOR+/_POV+/_POS+/_VOR=360^@# ( angles in a full circle )

#60^@+120^@+110^@+/_VOR=360^@#

#/_VOR=color(blue)(70^@)#

measure of arc SR #=/_SOR=color(blue)(60^@)#

measure of arc RV #=/_VOR=color(blue)(70^@)#

measure of arc PV #=/_POV=color(blue)(120^@)#

measure of arc PS #=/_POS=color(blue)(110^@)#

measure of arc SPV #=/_POS+/_POV=color(blue)(230^@)#

measure of arc VSP #=360^@-/_POV=color(blue)(240^@)#

measure of arc RPV #=360^@-/_VOR=color(blue)(290^@)#