O is the centre of a circle to which pax and pby are tangents from a point p at point a and b . Q is a point on the circle such that angle qax is 49 and qby is 62 what is the measure of angle aqb
Answers
Answer:
the answer isc51 degrees
Given : pax and pby are tangents from a point p at point a and b . Q is a point on the circle such that angle qax is 49 and qby is 62. O is center of circle
To find : measure of angle aqb
Solution:
∠qax = 49°
=> ∠paq = 180° - 49 ° = 131°
∠qby = 62°
= ∠pbq = 180° - 62 ° = 118°
in Quadrilateral apbq
∠paq + ∠aqb + ∠pbq + ∠apb = 360°
=> 131° + ∠aqb + 118° + ∠apb = 360°
=> ∠aqb + ∠apb = 111° Eq1
in Quadrilateral apbo
∠pao + ∠aob + ∠pbo + ∠apb = 360°
=> 90° + ∠aob + 90° + ∠apb = 360°
=> ∠aob + ∠apb = 180°
∠aob = 2 ∠aqb ( angle by same chord at center & arc segment )
=> 2 ∠aqb + ∠apb = 180° E2
Eq2 - Eq1
=> ∠aqb = 180° - 111°
=> ∠aqb = 69°
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