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The figure above shows two circles ABPQ and ABSR intersecting at A and B. QART, PBS and ABU are straight lines. The line TSU is...

The figure above shows two circles ABPQ and ABSR intersecting at A and B. QART, PBS and ABU are straight lines. The line TSU is a tangent to the circle ABSR at S. Given that ˂BPQ = 80^o, ˂PBU = 115^o and ˂BUS = 70^o.

Find & state reasons for the following angles
a) ˂BRS
b) ˂BSU
c) ˂STR
d) ˂BAR
e) ˂ARB

Answers

(a) 45⁰ – Angles at an alternate segment are equal
(b) 45⁰ – The sum of interior angles of a triangle add up to 180⁰
(c) 30⁰ – Sum of interior angles of a triangle add up to 180⁰
(d) ?BAR – 80⁰ The Opposite interior angles of a cycle quadrilateral are supplementary
(e) 20⁰ - ARS = 65 - Opposite angles of cycle qual are equal BRS = 45⁰ in (a) above
ARB = 65⁰- 45⁰ = 20⁰

Kavungya answered the question on November 12, 2019 at 10:37

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