Question

Can you help please I am struggling thank you

Answer 1

Answer:

m<ADC = 107

Step-by-step 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