inscribed angles 2

OPPOSITE angles of a cyclic quadrilateral ( a quadrilateral with all vertices on the circumference of a given circle) add to 180 degrees.....s o

 

x + (4x-20) = 180

5x=200

x = 40

 

B = 4x-20

       4(40) - 20 = 140 degrees

The opposite angles of a cyclic quadrilateral (a quadrilateral whose vertices touch the circumference of a circle) always add up to 180°.

Thus:

\(x+4x-20=180\)

\(5x-20=180\)

\(5x=180+20=200\)

\(x=\frac { 200 }{ 5 } =40\)

\(\angle B=(4x-20)°=(4\times 40-20)°=(160-20)°=140°\)

 

So, the measure of angle B is 140°.