Question

Please help me!

AEC = a. 72.5 b. 107.5 c. 63.5 d.116.5
The measures of angle EAD and ECD = a.72.5 b.58.25 c.90
ABC = a. 72.5 b. 90 c. 121.75 d.58.25
ADC = a. 107.5 b.116.5 c. 58.25 d. 63.5

Answer 1

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