Question

In Fig 8.105, AB, CD and ∠1 and ∠2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

Answer 1

∠1 = ∠3=∠5=∠7=108° and                                   ∠2= ∠4=∠6=∠8=72°

Step-by-step explanation:

• Given data

        $\mathbf{\frac{\angle 1}{\angle 2}=\frac{3}{2}}$

         Let

        ∠1 =3k

        ∠2=2k

• Where ∠1 and ∠2 are are adjacent angle for straight line AB,so

        ∠1 +∠2 = 180°  (Linear pair angle)

         3k + 2k =180°

         5k =180°

         $\mathbf{k=\frac{180^{\circ}}{5}=36^{\circ}}$

• Then

         ∠1 =3k = 3×36 = 108°

         ∠2 =2k = 2×36 = 72°

• Now

        ∠4 =∠2 = 72°       (Vertically opposite angle)

        ∠6 =∠2 = 72°       ( Corresponding angle)

        ∠8 =∠2 = 72°       ( Alternate exterior angle)

• Similarly

        ∠3 =∠1 = 108°       (Vertically opposite angle)

        ∠5 =∠1 = 108°       ( Corresponding angle)

        ∠7 =∠1 = 108°       ( Alternate exterior angle)

Answer 2

Question solved  

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