Answer:
[tex]m<D=106\°[/tex]
Step-by-step explanation:
we know that
In a quadrilateral inscribed in a circle opposite angles are supplementary so
[tex]m<A+m<C=180\°[/tex]
[tex]m<B+m<D=180\°[/tex]
Step 1
Find the value of x
substitute the values
[tex]x^{2} +3x=180\\ \\ x^{2} +3x-180=0[/tex]
using a graphing tool
solve the quadratic equation
see the attached figure
[tex]x=12\°[/tex]
step 2
Find the measure of angle D
[tex]m<B+m<D=180\°[/tex]
[tex]m<B=7x-10=7(12)-10=74\°[/tex]
substitute
[tex]74\°+m<D=180\°[/tex]
[tex]m<D=180\°-74\°=106\°[/tex]
