In the figure- AB is parallel to DC and AD is parallel to BC- If - ADC -105- - CBE - isA- 105-B- 75-C- 55-D- 90-

The correct option is B 75^∘ ∠ DAB = 180^∘ ∠ ADC = 180^∘ 105^∘ = 75^∘ [Co interior angles are supplementary] ∠ DAB = ∠ CBE= 75^∘ [Corresponding angles ar ...

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Standard VII

Mathematics

Corresponding Angles

In the figure...

Question

In the figure, AB is parallel to DC and AD is parallel to BC,

If $∠ A D C = 105^{\circ}, ∠ C B E = ?$ is

$105^{\circ}$

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$75^{\circ}$

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$55^{\circ}$

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$90^{\circ}$

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Solution

The correct option is B
$75^{\circ}$

$∠ D A B = 180^{\circ} - ∠ A D C = 180^{\circ} - 105^{\circ} = 75^{\circ}$ [Co-interior angles are supplementary]
$∠ D A B = ∠ C B E = 75^{\circ}$ [Corresponding angles are equal as AD is parallel to BC]
Hence, $∠ C B E = 75^{\circ} .$

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Similar questions

In the figure, ABCD is a parallelogram in which $∠ A D C = 105^{\circ}, ∠ C B E$ is

Q. In the figure, ABCD is a parallelogram in which

∠ A D C = 105^{\circ}

. The value of

∠ C B E

is ______.

In the figure, ABCD is a quadrilateral in which $\angle ADC=105^\circ ~and~ \angle ADC=~\angle ABC. Find \angle CBE$.

Q. In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that ∠ADC = 95° and ∠ECF = 20°. Then, ∠BAD = ?
(a) 95°
(b) 85°
(c) 105°
(d) 75°

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In the figure, AB is parallel to DC and AD is parallel to BC, If ∠ADC=105∘, ∠CBE=? is

The correct option is B 75∘ ∠DAB=180∘−∠ADC=180∘−105∘=75∘ [Co-interior angles are supplementary] ∠DAB=∠CBE=75∘ [Corresponding angles are equal as AD is parallel to BC] Hence, ∠CBE=75∘.

In the figure, AB is parallel to DC and AD is parallel to BC,

If $∠ A D C = 105^{\circ}, ∠ C B E = ?$ is

The correct option is B
$75^{\circ}$

$∠ D A B = 180^{\circ} - ∠ A D C = 180^{\circ} - 105^{\circ} = 75^{\circ}$ [Co-interior angles are supplementary]
$∠ D A B = ∠ C B E = 75^{\circ}$ [Corresponding angles are equal as AD is parallel to BC]
Hence, $∠ C B E = 75^{\circ} .$