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In the figure, ABCD is a parallelogram in which BAO={35}^{o},

Question

In the figure, $A BC D$ is a parallelogram in which $∠ B A O = 35^{o}, ∠ D A O = 40^{o}$ and $∠ CO D = 105^{o}$ . Calculate $∠ CB D$

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In the figure,

A BC D

is a parallelogram in which

∠ B A O = 35^{o}, ∠ D A O = 40^{o}

and

∠ CO D = 105^{o}

. Calculate

∠ CB D

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Text solutionVerified

We know that

∠ B

can be written as

∠ B = ∠ CB D + ∠ A BO

so we get

∠ CB D = ∠ B - ∠ A BO

In a parallelogram we know that the sum of all the angles is

360^{o}

so we get

∠ A + ∠ B + ∠ C + ∠ D = 360^{o}

it can be written as

2∠ A + 2∠ B = 360^{o}

by substituting values in abvoe equation

2 (40^{o} + 35^{o}) + 2∠ B = 360^{o}

2 (75^{o}) + 2∠ B = 360^{o}

150^{o} + 2∠ B = 360^{o}

2∠ B = 360^{o} - 150^{o}

∠ B = 105^{o}

so we get

∠ CB D = ∠ B - ∠ A BO

by substituting values

∠ CB D = 105^{o} - 40^{o}

∠ CB D = 65^{o}

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Question Text	In the figure, $A BC D$ is a parallelogram in which $∠ B A O = 35^{o}, ∠ D A O = 40^{o}$ and $∠ CO D = 105^{o}$ . Calculate $∠ CB D$
Answer Type	Text solution:1
Upvotes	150