Question

Please help me to solve this problem.
I have an answer also. But i don't know how to solve. ​

Answer 1

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Here, ∠ 1 + ∠ 4 = 180 ° ( Linear pair Axiom )

Let the ratios be X.

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Now,

∠ 1 + ∠ 4 = 180 °

⇒ X + 5X = 180 °

⇒ 6X = 180 °

⇒ X = 180 ÷ 6

⇒ X = 30 °

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Now,

• ∠ 1 = X = 30 °

• ∠ 4 = 5X = 30 × 5 = 150 °

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∠ 4 = ∠ 2 ( Vertically Opposite Angles )

Or, ∠ 2 = 150 °

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∠ 1 = ∠ 3 ( Vertically Opposite Angles )

Or, ∠ 3 = 30 °

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∠ 2 = ∠ 6 ( Corresponding Angles )

Or, ∠ 6 = 150 °

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∠ 6 = ∠ 8 ( Vertically Opposite Angles )

Or, ∠ 8 = 150 °

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∠ 1 = ∠ 5 ( Corresponding Angles )

Or, ∠ 5 = 30 °

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∠ 5 = ∠ 7 ( Vertically Opposite Angles )

Or, ∠ 7 = 30 °

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Please refer to the Attached image for Examples related to Angles. You'll be able to put it more clearly.

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Answer 2

Answer

We know that, the angles 1 and 4 are in the ratio of 1:5 and they are a pair of linear angles. So,

Value of ∠1 :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow \angle{1} + \angle{4} = {180}^{\circ}$

$\sf \dashrightarrow 1x + 5x = {180}^{\circ}$

$\sf \dashrightarrow 6x = {180}^{\circ}$

$\sf \dashrightarrow x = \dfrac{180}{6}$

$\sf \dashrightarrow x = 30$

$\sf \dashrightarrow \angle{1} = {30}^{\circ}$

Value of ∠2 :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow \angle{1} + \angle{2} = {180}^{\circ}$

$\sf \dashrightarrow {30}^{\circ} + \angle{2} = {180}^{\circ}$

$\sf \dashrightarrow \angle{2} = 180 - 30$

$\sf \dashrightarrow \angle{2} = {150}^{\circ}$

Value of ∠3 :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow \angle{2} + \angle{3} = {180}^{\circ}$

$\sf \dashrightarrow {150}^{\circ} + \angle{3} = {180}^{\circ}$

$\sf \dashrightarrow \angle{3} = 180 - 150$

$\sf \dashrightarrow \angle{3} = {30}^{\circ}$

Value of ∠4 :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow \angle{3} + \angle{4} = {180}^{\circ}$

$\sf \dashrightarrow {30}^{\circ} + \angle{4} = {180}^{\circ}$

$\sf \dashrightarrow \angle{4} = 180 - 30$

$\sf \dashrightarrow \angle{4} = {150}^{\circ}$

Value of ∠5 :

$\sf \dashrightarrow Interior \: angles \: on \: same \: side = {180}^{\circ}$

$\sf \dashrightarrow \angle{4} + \angle{5} = {180}^{\circ}$

$\sf \dashrightarrow {150}^{\circ} + \angle{5} = {180}^{\circ}$

$\sf \dashrightarrow \angle{5} = 180 - 150$

$\sf \dashrightarrow \angle{5} = {30}^{\circ}$

Value of ∠6 :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow \angle{5} + \angle{6} = {180}^{\circ}$

$\sf \dashrightarrow {30}^{\circ} + \angle{6} = {180}^{\circ}$

$\sf \dashrightarrow \angle{6} = 180 - 30$

$\sf \dashrightarrow \angle{6} = {150}^{\circ}$

Value of ∠7 :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow \angle{6} + \angle{7} = {180}^{\circ}$

$\sf \dashrightarrow {150}^{\circ} + \angle{7} = {180}^{\circ}$

$\sf \dashrightarrow \angle{7} = 180 - 150$

$\sf \dashrightarrow \angle{7} = {30}^{\circ}$

Value of ∠8 :

$\sf \dashrightarrow Straight \: line \: angle = {180}^{\circ}$

$\sf \dashrightarrow \angle{7} + \angle{8} = {180}^{\circ}$

$\sf \dashrightarrow {30}^{\circ} + \angle{8} = {180}^{\circ}$

$\sf \dashrightarrow \angle{8} = 180 - 30$

$\sf \dashrightarrow \angle{8} = {150}^{\circ}$