In the given figure AB DC and AD BC- ADC -2 x -5- and - BCD -3 x -55-then x - -A- 28-B- 45-C- 20-D- 24-

The correct option is D 24^∘ AB ∥ DC and AD ∥ BC ∠ ADC + ∠ BCD = 180^∘ ( Sum of Co interior angles) (2x+5) + nbsp;(3x+55) = 180 (2x+3x) + nbsp;(5+55) = 1 ...

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Standard VII

Mathematics

Ray

In the given ...

Question

In the given figure

$A B ∥ D C a n d A D ∥ B C$

$∠ A D C = (2 x + 5)^{\circ} a n d ∠ B C D = (3 x + 55)^{\circ}$

then x = ?

$28^{\circ}$

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$45^{\circ}$

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$20^{\circ}$

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$24^{\circ}$

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Solution

The correct option is D
$24^{\circ}$

$A B ∥ D C a n d A D ∥ B C$

$∠ A D C + ∠ B C D = 180^{\circ} (S u m o f C o - i n t e r i o r a n g l e s)$

$(2 x + 5) + (3 x + 55) = 180$

$(2 x + 3 x) + (5 + 55) = 180$

$(5 x) + (60) = 180$

$5 x = 180 - 60$

$5 x = 120$

$x = 24^{\circ}$

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Similar questions

In the given figure, $A B ∥ D C a n d A D ∥ B C$ .

Also, $∠ A D C = (2 x + 5)^{\circ} a n d ∠ B C D = (3 x + 55)^{\circ}$ . Find the measure of x.

In the given figure, ABCD is a quadrilateral in which AB || DC and AD || BC.
Prove that ∠ADC = ∠ABC.

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(a) 32°
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In the given figure AB∥DC and AD∥BC ∠ADC=(2x+5)∘ and ∠BCD=(3x+55)∘ then x = ?

The correct option is D 24∘ AB∥DC and AD∥BC ∠ADC+∠BCD=180∘ (Sum of Co−interior angles) (2x+5)+(3x+55)=180 (2x+3x)+(5+55)=180 (5x)+(60)=180 5x=180−60 5x=120 x=24∘

In the given figure

$A B ∥ D C a n d A D ∥ B C$

$∠ A D C = (2 x + 5)^{\circ} a n d ∠ B C D = (3 x + 55)^{\circ}$

then x = ?

The correct option is D
$24^{\circ}$

$A B ∥ D C a n d A D ∥ B C$

$∠ A D C + ∠ B C D = 180^{\circ} (S u m o f C o - i n t e r i o r a n g l e s)$

$(2 x + 5) + (3 x + 55) = 180$

$(2 x + 3 x) + (5 + 55) = 180$

$(5 x) + (60) = 180$

$5 x = 180 - 60$

$5 x = 120$

$x = 24^{\circ}$