In the given figure- nbsp-AC nbsp-is a diameter of the circle- Find the value of x- 136-100-126-154-

The correct option is C 126^∘Since angle in a semicircle is a right angle, we have ∠ ABC=90^∘. But, ∠ ABD nbsp;+ ∠ DBC nbsp;= ∠ ABC i.e., ∠ ABD nbsp;+ 36 ...

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Byju's Answer

Standard X

Mathematics

Exterior Angle of Cyclic Quadrilateral

In the given ...

Question

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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Similar questions

Question 30

In the given figure, lines PQ and ST intersect at O. If $∠ P O R = 90^{\circ}$ and
x:y = 3:2, then z is equal to

(a) $126^{\circ}$
(b) $144^{\circ}$
(c) $136^{\circ}$
(d) $154^{\circ}$