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in Lines and Angles by (56.3k points)

In figure, AB, CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

1 Answer

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Best answer

Let ∠1 = 3x and ∠2 = 2x

From figure: ∠1 and ∠2 are linear pair of angles 

Therefore, ∠1 + ∠2 = 180°

3x + 2x = 180°

5x = 180°

x = 180/5 

=> x = 36° 

So, ∠1 = 3x = 108° and ∠2 = 2x = 72° 

As we know, vertically opposite angles are equal. 

Pairs of vertically opposite angles are: 

(∠1 = ∠3); (∠2 = ∠4) ; (∠5, ∠7) and (∠6 , ∠8) 

∠1 = ∠3 = 108° 

∠2 = ∠4 = 72° 

∠5 = ∠7 

∠6 = ∠8 

We also know, if a transversal intersects any parallel lines, then the corresponding angles are equal 

∠1 = ∠5 = ∠7 = 108° 

∠2 = ∠6 = ∠8 = 72° 

Answer: ∠1 = 108°, ∠2 = 72°, ∠3 = 108°, ∠4 = 72°, ∠5 = 108°, ∠6 = 72°, ∠7 = 108° and ∠8 = 72°.

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