Question

In circle O below, AB is the diameter, angle BOD contains 15degrees, and angle EOA contains 85degrees. Find the number of degrees in angle ECA.

Answer 1

Ok from that information you should know the size of arcs AB and DB. If you know those there is a formula that will allow you to find the angle formed by two secants that meet outside of the circle.

Answer 2

Let's analyze this. AC is a straight angle, which implies that ∠EOA + ∠DOE + ∠BOD = 180º. From this, we obtain that ∠DOE = 80º. Since line segments OD and OE are radii, ΔODE is isosceles. This implies that ∠ODE = ∠OED = 50º. EC is a straight angle, which implies that ∠ODE + ∠ODC = 180º. Thus ∠ODC = 180º - 50º = 130º. In ΔCOD, ∠ODC + ∠COD + ∠DCO = 180º. Recognize that ∠COD = ∠BOD. Thus ∠DCO = ∠ECA = 35º

Answer 3

@calculusfunctions That was nice of you to do the whole problem for her so she didn't even have to think about that.

Answer 4

thank you @calculusfunctions
thanks everyon