-CD- ABC - x and - ADC -2 x - Find - CODA- XB- 180-3 xC- 180- xD- 2 x

The correct option is B 180 – 3x In AOB and DOC, AB||CD Therefore, ∠ ABO = ∠ DCO = x and ∠ BAO = ∠ CDO = 2x ex (alternate interior angles) ∠ AOB = ∠ DOC ex ( ...

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Byju's Answer

Standard X

Mathematics

AAA Similarity

||CD∠ ABC = x...

Question

$∠ A B C = x a n d ∠ A D C = 2 x$ . Find $∠ C O D$

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180 – 3x

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180 - x

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Solution

The correct option is C
180 – 3x

$I n △ A O B a n d △ D O C, A B | | C D$
Therefore, $∠ A B O = ∠ D C O = x a n d ∠ B A O = ∠ C D O = 2 x$ (alternate interior angles)
$∠ A O B = ∠ D O C$ (vertically opposite angles)
Therefore, $△ A O B \sim △ D O C$ by AA similarity
So, $∠ A O B = ∠ D O C = 180 - 3 x$ (angle sum property)

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∠ABC=x and ∠ADC=2x. Find ∠COD

The correct option is C 180 – 3x In △AOB and △DOC,AB||CD Therefore, ∠ABO=∠DCO=x and ∠BAO=∠CDO=2x (alternate interior angles) ∠AOB=∠DOC (vertically opposite angles) Therefore, △AOB∼△DOC by AA similarity So, ∠AOB=∠DOC=180−3x (angle sum property)

$∠ A B C = x a n d ∠ A D C = 2 x$ . Find $∠ C O D$