In the figure- ABCD is parallelogram in which - ADC- 105- The value of - CBE is

ABCD is a parallelogram ∴, ∠ ADC = ∠ ABC = 105^∘ [Opposite angles of a parallelogram are equal] ∠ ABC +∠ CBE = 180^∘ [Linear pair] ∠ CBE = 180^∘ 105^∘ = 75^ ...

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Standard VIII

Mathematics

Angle Sum Property of a Quadrilateral

In the figure...

Question

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

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Solution

ABCD is a parallelogram
$∴, ∠ A D C = ∠ A B C = 105^{\circ}$
[Opposite angles of a parallelogram are equal]
$∠ A B C + ∠ C B E = 180^{\circ} [L i n e a r p a i r] ∠ C B E = 180^{\circ} - 105^{\circ} = 75^{\circ} H e n c e, ∠ C B E = 75^{\circ}$

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In the figure, ABCD is parallelogram in which ∠ADC=105∘. The value of ∠CBE is

ABCD is a parallelogram ∴, ∠ADC=∠ABC=105∘ [Opposite angles of a parallelogram are equal] ∠ABC+∠CBE=180∘[Linear pair]∠CBE=180∘−105∘=75∘Hence, ∠CBE=75∘

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

ABCD is a parallelogram
$∴, ∠ A D C = ∠ A B C = 105^{\circ}$
[Opposite angles of a parallelogram are equal]
$∠ A B C + ∠ C B E = 180^{\circ} [L i n e a r p a i r] ∠ C B E = 180^{\circ} - 105^{\circ} = 75^{\circ} H e n c e, ∠ C B E = 75^{\circ}$