A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of v when angle D is 140 degrees? Choose one.
A) 20
B) 40
C) 60
D) 80
E) 100
An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.   An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.   angle D = 140 degrees   Thus,   arc ABC = 280 degrees   A whole circle has 360 degrees of arc, so arc ADC should be the rest of the circle.   arc ADC = 360 - 280= 
<gadget id="calculator">360 - 280</gadget>
<output>80</output>
80 degrees   The angle that intersects this arc, angle B, should have half this measure.   angle 40= v = 80/2= 
<gadget id="calculator">80/2</gadget>
<output>40</output>
40 degrees   Answer=(40)
<result>B</result>
A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of v when angle D is 140 degrees?