Question

Remember that arc DAB will be twice as large as mC. If m A= 109, then what is the degree measure of arc DAB?

Answer 1

Opposite angles in a cyclic quadrilateral always sum up to 180º.

Angle A is opposite to angle C.

$\begin{gathered} m\angle A+m\angle C=180º \\ \end{gathered}$

Use the equation above to find the measure of angle C:

$\begin{gathered} m\angle C=180º-m\angle A \\ m\angle C=180º-109º \\ m\angle C=71º \end{gathered}$

As arc DAB is twice as large as measure of angle C:

$\begin{gathered} \text{DAB}=2(m\angle C) \\ \text{DAB}=2(71º) \\ \text{DAB}=142º \end{gathered}$Then, the degree measure of arc DAB is 142º