[tex]7)\:x=30\:8)x=10\:9)\:x=8[/tex]
7) We have here intersecting chords, so we can find the measure of the arcs and angles with this formula:
[tex]\begin{gathered} m\angle AED=\frac{1}{2}(mAD+mCB) \\ 5x-90=\frac{1}{2}(3x+x) \\ 5x-90=2x \\ 5x-90+90=2x+90 \\ 5x=2x+90 \\ 3x=90 \\ \frac{3x}{3}=\frac{90}{3} \\ x=30 \end{gathered}[/tex]
8) Focusing on the circle below that, we can do the same:
[tex]\begin{gathered} m\angle AEC=\frac{1}{2}(mAC+mBD) \\ 7x+50=\frac{1}{2}(8x+4x+120) \\ 7x+50=6x+60 \\ 7x=6x+10 \\ 7x-6x=6x+10-6x \\ x=10 \end{gathered}[/tex]
9) And finally, we can do that since the same case presents here:
[tex]\begin{gathered} m\angle BED=\frac{1}{2}(mAC+mBD) \\ 10x+40=\frac{1}{2}(14x-32+20x) \\ 10x+40=17x-16 \\ 10x+40-40=17x-16-40 \\ 10x=17x-56 \\ 10x-17x=17x-56-17x \\ -7x=-56 \\ \frac{-7x}{-7}=\frac{-56}{-7} \\ x=8 \end{gathered}[/tex]
