Question

Determine the number of degrees in these arcs?

Answer 1

a.

Let's call the intersection point of the chords M.

In order to calculate the arc AB, we can use the following property:

`\angle AMB=(AB+CD)/(2)`

Since ∠AMB is 86° and CD = 30°, we have:

`\begin{gathered} 86=(AB+30)/(2) \\ AB+30=172 \\ AB=172-30 \\ AB=142\degree \end{gathered}`

b.

In order to find DC, let's use the same formula, with ∠AMB = 86° and AB = 135°:

`\begin{gathered} 86=(135+DC)/(2) \\ 135+DC=172 \\ DC=172-135 \\ DC=37\degree \end{gathered}`