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

Question

In Fig 8.105, AB, CD and &#x2220; 1 and &#x2220; 2 are in the ratio 3 : 2. Determine all angles from 1 to 8.

Philoid · Accepted Answer

Let, ∠1 = 3x

∠2 = 2x

∠1 + ∠2 = 180^o(Linear pair)

3x + 2x = 180^o

5x = 180^o

x = 36^o

Therefore,

∠1 = 3x = 108^o

∠2 = 2x = 72^o

Vertically opposite angles are equal, so:

∠1 = ∠3 = 108^o

∠2 = ∠4 = 72^o

∠5 = ∠7 = 108^o

∠6 = ∠8 = 72^o

Corresponding angles:

∠1 = ∠5 = 108^o

∠2 = ∠6 = 72^o