Question

​ Quadrilateral ABCD ​ is inscribed in this circle.

Answer 1

Answer: $m\angle A=116\°$

Step-by-step explanation:

The missing figure is attached.

For this exercise it is important to remember that, by definition, the opposite interior angles of an inscribed quadrilateral are supplementary, which means that their sum is 180 degrees.

Based on this, you can identify that the angle D and the angle B are opposite and, therefore, supplementary.

Knowing that, you can write the following equation:

$x+28\°=180\°$

Now you must solve for "x" in order to find its value. This is:

$x=180\°-28\°\\\\x=152\°$

Then:

$m\angle D=152\°$

You know that:

$m\angle A=(x-36)\°$

Therefore, since you know the value of "x", you can substitute it into   $m\angle A=(x-36)\°$ and then you must evaluate, in order to find the measure of the angle A. This is:

 $m\angle A=152\°-36\°\\\\m\angle A=116\°$