Answer:
[tex]m<D=98\°[/tex]
Step-by-step explanation:
we know that
The Inscribed Quadrilateral Theorem, states that a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary
so
In this problem
[tex]m<A+m<C=180\°[/tex] -----> equation A
[tex]m<B+m<D=180\°[/tex] -----> equation B
we have
[tex]m<A=64\°[/tex]
[tex]m<B=(6x+4)\°[/tex]
[tex]m<C=(9x-1)\°[/tex]
Step 1
Find the value of x
substitute the measure of angle A and the measure of angle C in the equation A to find x
[tex]64\°+(9x-1)\°=180\°[/tex]
[tex]9x=180\°-64\°+1\°[/tex]
[tex]9x=117\°[/tex]
[tex]x=13\°[/tex]
Step 2
Find the measure of angle D
substitute the measure of angle B in the equation B to find m<D
[tex](6x+4)+m<D=180\°[/tex]
substitute the value of x
[tex](6(13)+4)+m<D=180\°[/tex]
[tex]82\°+m<D=180\°[/tex]
[tex]m<D=180\°-82\°=98\°[/tex]
