Answer:
m<ADC = 107
Explanation:
You need to know three things to solve this problem.
1) Opposite angles of an inscribed quadrilateral are supplementary.
2) The measure of an inscribed angle is half the measure of its subtended arc.
3) The sum of the measures of all the arcs of a circle is 360 deg.
From 1) we get:
m<A + m<C = 180
72 + m<C = 180
m<C = 108
From 2) we get:
m<C = (1/2)m(arc)BAD
108 = (1/2)[m(arc)AB + m(arc)AD]
216 = m(arc)AB + 122
m(arc)AB = 94
From 3) we get:
m(arc)AB + m(arc)BC + m(arc)CD + m(arc)DA = 360
94 + 120 + m(arc)CD + 122 = 360
m(arc)CD = 24
From 2) we get:
m<ADC = (1/2)m(arc)ABC
m<ADC = (1/2)[m(arc)AB + m(arc)BC]
m<ADC = (1/2)[94 + 120]
m<ADC = 107