Question

AB is a diameter of the circle with centre O. BT is a tangent. AC produced meets tangent BT at T.
If angle ABC = 38°, find angle T.
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Answer 1

Step-by-step explanation:

AB is the straight line

∠AOQ+∠BOQ=180

o

∠BOQ=180

o

−58

∠BOQ=122

o

In triangle BOQ,OB+OQ are equal since they are radius of the circle (OB=OQ)

So ∠OBQ=∠OQB (Since sides opposite are equal angle opposite to the equal sides are equal)

So ∠OBQ+∠OQB+∠BOQ=180

o

122

o

+2(∠OBQ)=180

o

→∠OBW=29

o

In triangle ABT⇒∠ABT+∠BAT+∠BTA=180

o

=29

o

+90

o

+∠BAT=180

o

∠ATQ=61

o