In the given figure- AB - DC and AD - BC-Also- - ADC - 2x-5- and - BCD - 3x-55- Find the measure of x-3 marks

AB ∥ DC and AD ∥ BC ∠ ADC + ∠ BCD = 180^∘ ( Sum of Co interior angles) ⇒ (2x+5^∘) + nbsp;(3x+55^∘) = 180^∘ (1 mark) = (2x+3x) + nbsp;(5^∘ + 55^∘) = 18 ...

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Standard IX

Mathematics

Adjacent Angles

In the given ...

Question

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.

(3 marks)

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Solution

$A B ∥ D C a n d A D ∥ B C$

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

⇒ $(2 x + 5^{\circ}) + (3 x + 55^{\circ}) = 180^{\circ}$
(1 mark)

= $(2 x + 3 x) + (5^{\circ} + 55^{\circ}) = 180^{\circ}$

= $(5 x) + (60^{\circ}) = 180^{\circ}$

= $5 x = 180^{\circ} - 60^{\circ}$

= $5 x = 120^{\circ}$

=> $x = 24^{\circ}$
(2 marks)

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In the given figure, AB∥DC and AD∥BC. Also, ∠ADC=(2x+5)∘ and ∠BCD=(3x+55)∘. Find the measure of x. (3 marks)

AB∥DC and AD∥BC ∠ADC+∠BCD=180∘ (Sum of Co−interior angles) ⇒ (2x+5∘)+(3x+55∘)=180∘ (1 mark) = (2x+3x)+(5∘+55∘)=180∘ = (5x)+(60∘)=180∘ = 5x=180∘−60∘ = 5x=120∘ => x=24∘ (2 marks)

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.

(3 marks)