In the given figure, AC is a diameter of the circle. Find the value of $x .$

100^{\circ}

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126^{\circ}

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136^{\circ}

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154^{\circ}

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Solution

The correct option is B $126^{\circ}$
Since angle in a semicircle is a right angle, we have
$∠ A B C = 90^{\circ} .$
But, $∠ A B D + ∠ D B C = ∠ A B C$
i.e., $∠ A B D + 36^{\circ} = 90^{\circ}$
$⟹ ∠ A B D = 54^{\circ}$
Consider the cyclic quadrilateral ABDE. Since opposite angles are supplementary, we have
$∠ A B D + x = 180^{\circ}$
$⟹ x = 180^{\circ} - 54^{\circ} = 126^{\circ}$

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In the given figure, AB is the diameter of the circle. AC is equal to BC. Find the value of $∠ A B C$ .

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In the given figure, AC is a diameter of the circle. Find the value of x.

The correct option is B 126∘Since angle in a semicircle is a right angle, we have ∠ABC=90∘. But, ∠ABD+∠DBC=∠ABC i.e., ∠ABD+36∘=90∘ ⟹∠ABD=54∘ Consider the cyclic quadrilateral ABDE. Since opposite angles are supplementary, we have ∠ABD+x=180∘ ⟹x=180∘–54∘=126∘

In the given figure, AC is a diameter of the circle. Find the value of $x .$