General Idea:
A cyclic quadrilateral has all its vertices on the circumference of the circle. The opposite angles of a cyclic quadrilateral are supplementary, that is it add up to get 180 degrees.
Applying the Concept:
Opposite angles B and D add up to give 180 degrees.
[tex] \angle B + \angle D=180\\ \\ 4x-20+x=180\\ Grouping \; like \; terms\\ \\ 4x+x-20=180\\ Combining \; like\; terms\\\\ 5x-20 =180\\ Adding \; 20 \; on\; both\; sides\\ \\ 5x-20+20=180+20\\ Combine\; like\; terms\\ \\ 5x=200\\ Divide\; 5\; on\; both\; sides\\ \\ \frac{5x}{5} =\frac{200}{5} \\ Simplify \; fraction\; on\; both\; sides\\ \\ x=40\\ \\ Substitute \; 40\; for\; x\; in\; the\; expression\; for\; \angle B \\ \angle B=4x-20=4(40)-20=160-20\\\\\angle B=140 [/tex]
Conclusion:
When Quadrilateral ABCD is inscribed in this circle, the measure of angle B for the given diagram is [tex] 140^{\circ} [/tex]
