In the figure given below- find x if AB CD-A- 45-B- 55-C- 60-D- 70-

The correct option is B 55^∘ From the given figure, ∠ ECD nbsp;= 180^∘ nbsp; 150^∘ nbsp;= 30^∘ nbsp;(sum of interior angles on the same side of the tra ...

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Standard X

Mathematics

Angles in Alternate Segments

In the figure...

Question

In the figure given below, find $x$ if AB || CD.

45 $^{\circ}$

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55 $^{\circ}$

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60 $^{\circ}$

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70 $^{\circ}$

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Solution

The correct option is B
55 $^{\circ}$

From the given figure,

$∠ E C D = 180^{\circ} - 150^{\circ} = 30^{\circ}$ (sum of interior angles on the same side of the transversal is 180°)

$x = ∠ B C D = 25^{\circ} + ∠ E C D$ (alternate interior angles)
$= 25^{\circ} + 30^{\circ} = 55^{\circ}$

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Similar questions

In the figure given below, find $x$ if AB || CD || EF.

Question 3

In the given figure, PQ = PS. The value of x is

a) $35^{\circ}$
b) $45^{\circ}$
c) $55^{\circ}$
d) $70^{\circ}$

In the given figure, AB||CD. If $∠ E A B = 50^{\circ}$ and $∠ E C D = 60^{\circ}$ then $∠ A E B = ?$

$(a) 50^{\circ}$

$(b) 60^{\circ}$

$(c) 70^{\circ}$

$(d) 55^{\circ}$

Q. In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If

∠ T P Q = 70 °,

find

∠ T R Q .

In the given figure,

∠

ABO = 45

^{\circ}

and

∠

BAO = 75

^{\circ}

. If

∠

OCD = 70

^{\circ}

, what is the value of

∠

ODC?

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In the figure given below, find x if AB || CD.

The correct option is B 55∘ From the given figure, ∠ECD=180∘−150∘=30∘ (sum of interior angles on the same side of the transversal is 180°) x=∠BCD=25∘+∠ECD (alternate interior angles) =25∘+30∘=55∘

In the figure given below, find $x$ if AB || CD.

The correct option is B
55 $^{\circ}$

From the given figure,

$∠ E C D = 180^{\circ} - 150^{\circ} = 30^{\circ}$ (sum of interior angles on the same side of the transversal is 180°)

$x = ∠ B C D = 25^{\circ} + ∠ E C D$ (alternate interior angles)
$= 25^{\circ} + 30^{\circ} = 55^{\circ}$