Answer:
<BAD = 92°, <BCD = 88°, <ADC = 80°, <ABC = 100°
Step-by-step explanation:
According to the inscribed quadrilateral conjecture, the sum of each two opposite angles inside of a quadrilateral that is inscribed by a circle is 180 degrees.
Thus, we can say that the sum of angles <BAD and <BCD is 180 degrees.
[tex]< \text{BAD } + < \text{BCD} = 180 \text{ // Substitute}\\(x + 2) + (x - 2) = 180 \text{ // Simplify}\\2x = 180\text{ //}\div2\\x = 90^\circ[/tex]
The value of x is 90.
We can then substitute x's value (90) into each of the angles to find their measurements.
[tex]< \text{BAD} = x + 2 = 90 + 2 = 92^\circ\\ < \text{BCD} = x - 2 = 90 - 2 = 88^\circ\\ < \text{ADC} = x - 10 = 90 - 10 = 80^\circ[/tex]
Finally, we can use the inscribed quadrilateral conjecture once again to find the value of angle ABC.
[tex]< \text{ABC }+\text{ADC} = 180\\ < \text{ABC }+80=180\text{ //}-80\\ < \text{ABC}=100^\circ[/tex]
