Please solve q 69 ?

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Answer 1 · 2018-05-13T18:38:23

$∠ B T C = 44^{\circ}$ $/_BTC=44^@$

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$∠ A C S = ∠ A B C = 67^{\circ}$ $/_ACS=/_ABC=67^@$ because they both face arc $A C$ $AC$ and are half the measure of that arc.

$∠ B A C = 90^{\circ}$ $/_BAC=90^@$ because it is an inscribed angle facing the diameter of the circle.

$∠ B C T = 180^{\circ} - (90^{\circ} + 67^{\circ}) = 23^{\circ}$ $/_BCT=180^@-(90^@+67^@)=23^@$

$∠ A B C = ∠ B T C + ∠ B C T$ $/_ABC=/_BTC+/_BCT$ because $∠ A B C$ $/_ABC$ is the exterior angle of triangle $DeltaBTC$ .

$67^@=/_BTC+23^@$

$/_BTC=67^@-23^@=44^@$