In the figure- A B C D is a quadrilateral in which - A D C-105- and - ADC - ABC - F ind - CBE-A- 105-B- 75-C- 55-D- 90-

The correct option is B Given ∠ ADC = 105^∘ and ∠ ADC= ∠ ABC ∴ ∠ ABC =105^∘ ∠ ABC+∠ CBE=180^∘ (∵ exterior angle + interior angle = 180^∘) ∠ CBE=180^∘ 105^∘= ...

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Byju's Answer

Standard VIII

Mathematics

Exterior and Interior Points to an Angle

In the figure...

Question

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

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Solution

The correct option is B
Given $∠ A D C = 105^{\circ}$ and $∠ A D C = ∠ A B C$

$∴ ∠ A B C = 105^{\circ}$
$∠ A B C + ∠ C B E = 180^{\circ}$ ( $∵ e x t e r i o r a n g l e + i n t e r i o r a n g l e = 180^{\circ}$ )
$∠ C B E = 180^{\circ} - 105^{\circ} = 75^{\circ}$
Hence, $∠ C B E = 75^{\circ} .$

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

The correct option is B Given ∠ADC = 105∘ and ∠ADC= ∠ABC ∴ ∠ABC =105∘ ∠ABC+∠CBE=180∘ (∵exterior angle+interior angle=180∘) ∠CBE=180∘−105∘=75∘ Hence, ∠CBE=75∘.