$T P$ and $T Q$ are the tangents to a circle, with centre $O .$ Find $x .$

15^{\circ}

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60^{\circ}

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30^{\circ}

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45^{\circ}

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Solution

The correct option is C $30^{\circ}$
In quadrilateral, OPTQ
$∠ O P T = ∠ O Q T = 90^{\circ}$ (Angle between radius and the tangent)
Sum of angles $= 360^{\circ}$
$∠ O P T + ∠ O Q T + ∠ P O Q + ∠ P T Q = 360^{\circ}$
$90^{\circ} + 90^{\circ} + x + 5 x = 360^{\circ}$
$6 x = 180^{\circ}$
$x = 30^{\circ}$

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TP and TQ are the tangents to a circle, with centre O. Find x.

The correct option is C 30∘In quadrilateral, OPTQ∠OPT=∠OQT=90∘ (Angle between radius and the tangent)Sum of angles =360∘∠OPT+∠OQT+∠POQ+∠PTQ=360∘90∘+90∘+x+5x=360∘6x=180∘x=30∘

$T P$ and $T Q$ are the tangents to a circle, with centre $O .$ Find $x .$