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AG is tangent to circle F at point A. if m<gac = 75, mAD = 52 and mAB = 88, find m<DEC

User Voivoid
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1 Answer

2 votes
the complete question in the attached figure

we know that

step 1
find the measure of arc AC
we know that
The inscribed angle measures half of the arc it comprises.
so
m∠GAC=(1/2)*[arc AC]
m∠GAC=75°
(1/2)*arc AC=75°-----> arc AC=150°

step 2
find the arc DC
arc AC=arc AD+arc DC
arc DC=arc AC-arc AD----> arc DC=150°-52°----> arc DC=98°

step 3
find m∠DEC

we know that
The measure of the interior angle is the half-summit of the arcs that comprise it and its opposite.
so
m∠DEC=(1/2)*[arc AB+arc DC]

arc AB=88°
arc DC=98°

m∠DEC=(1/2)*[88+98]----->
m∠DEC=93°

the answer is
m∠DEC=93°


AG is tangent to circle F at point A. if m<gac = 75, mAD = 52 and mAB = 88, find-example-1
User Paul Weber
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