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

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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