SOLUTION: Points A, B, Q, D, and C lie on the circle as shown and the measures of arcs BQ and QD are 42° and 38° respectively. What is the sum of the angles P and Q? https://assoc

Question 1132329:
Points A, B, Q, D, and C lie on the circle as shown and the measures of arcs BQ and QD are 42° and 38° respectively. What is the sum of the angles P and Q?

https://associations.missouristate.edu/assets/Math/Practice_Probs_Sept_2013_-_Solutions.pdf
Question 4 - Can someone explain this?/

Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
It is a property of circles and secants that if two secants intersect outside of the circle (PB and PD) the angle formed (angle P) will be 1/2 the difference of the two intercepted arcs: angle P = 1/2(arc_BD - arc_AC)

Angle Q is 1/2 arc_AC (inscribed angles are 1/2 their central angle)

angle P + angle Q = (1/2)(arc_AC) + (1/2)(arc_BD - arc_AC) = (1/2)(arc_BD) = (1/2)(80) = 40 degrees

Remember, the angle of an arc is the central angle that it sweeps, none of which are drawn on the Question 4 diagram

RELATED QUESTIONS
Points A, B, C, and D, lie on a circle. If the ratio of the arcs determined by these... (answered by ankor@dixie-net.com)

IF POINTS A,B,AND C LIE ON A CORDINATE LINE AND POINTS A AND B HAVE COORDINATES 15 AND 7... (answered by stanbon)

If points A,B and C lie on a coordinate line and points A and B have coordinates of 15... (answered by Edwin McCravy)

If points A, B, and C lie on a coordinate line and points A and B have coordinates 15 and (answered by scott8148)

If points A,B, and C lie on a coordinate line and points A and B have coordinates 15 and... (answered by kamallohia)

Somebody please help me with this problem... and thank you in advance!! USING... (answered by venugopalramana)

Question 8 If AB = 5.5, CD = 7, and FE = 19.5, calculate the values of line... (answered by MathLover1)

In triangle ABC the lines BQ and CR are perpendicular to AC and AB respectively. If... (answered by Edwin McCravy)

Could someone outline a strategy for solving the following problem? *Let \( \triangle... (answered by CPhill)