Question

In a cyclic = A B C D , twice the measure of
LA is thrice the measure of LC find the
measure of LC ?​

Answer 1

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➠ In a cyclic quadrilateral ABCD , twice the measure of  ∠A is thrice the measure of ∠C find the  measure of ∠C ?​

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❏ Cyclic Quadrilateral is a closed quadrilateral which is inscribed in a circle. In shorts all the 4 vertices of quadrilateral lies on same circle.

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❏ Sum of opposite angles of cyclic quadrilateral = 180°

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➠ 2∠A = 3∠C

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Let's Start !

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Let's use the following property of cyclic Quadrilateral.

❖ Sum of opposite angles of cyclic quadrilateral = 180°

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$:\implies \angle A + \angle C = 180^{ \circ}$

$:\implies \dfrac{3}{2} \angle C + \angle C = 180^{ \circ}$

$:\implies 3\angle C + 2\angle C = 360^{ \circ}$

$:\implies 5\angle C = 360^{ \circ}$

$\boxed { \red {:\implies \angle C = 72^{ \circ} } }$  

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$\boxed{\boxed{\bold{\therefore Angle \; C = 72^{\circ} }}}$

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Hope this helps u.../

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