Question

Please help me!

Answer 1

Answer:

Step-by-step explanation:

Nice summary problem.

<AEC

• AEC = 360 - 243.5 = 116.5    
• The number of degrees in 1 rotation of a circle = 360o. You have accounted for 243.5 degrees. What is left over is the answer.

<EAD and <ECD

Both of these are tangents to a circle. Tangents meet radii at 90 degree angles.

<EAD = <ECD = 90 degrees

<ABC

<ABC is 1/2 the central angle. The Central angle is <AEC

• < AEC = 116.5
• <ABC = 1/2 * 116.5
• <ABC = 58.25

<ADC

There are 2 ways of doing this. You should know both of them.

One

All quadrilaterals = 360 degrees. You know three of the angles. You should be able to find ADC

• <ADC + 90 + 90 + 116.5 = 360     Add the four angles together.
• <ADC + 296.5 = 360                   Combine terms on the left
• <ADC = 360 - 296.5                    Subtract 238.25 from both sides
• <ADC = 63.5                                 Answer

Method Two

<ADC = 1/2 (major Arc - Minor Arc)  This formula is fundamental to circle / tangent properties. The Major arc is the larger of the two parts of the circumference of a circle. The Minor arc is the smaller.

• <ADC = 1/2(243.5 - 116.5)
• <ADC = 1/2(127)
• <ADC = 63.5