Question

Quadrilateral ABCD ​ is inscribed in this circle.

Answer 1

The meaning of a quadrilateral inscribed in a circle is that the angles on the opposite vertices are supplementary or in other words equals to 180 degrees.

In this exercise it is asked you to find the measure in degrees of angle A. First of all, you have to find the value of x. To do this you have to select two angles, on this case angles B and D.

m<B+m<D=180        Substitute the given values of angles B and D
         28+x=180        Subtract in both sides by 28
               x=152

Now that the value of x is known, you can substitute it into the expression representing angle A.

m<A=x-36
m<A=152-36
m<A=116

The measure of angle A is 116 degrees.