Question

in the figure AB llCD and angle 1 and angle 2 are in the ratio 3 : 2 determine all angle from 1 to 8​

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Note = I am considering TQ in place of AB

∠1 : ∠2 = 3 : 2

Assume

∠1 = 3p

∠2 = 2p

Line “Y” stands on the line T

∠1 + ∠2 = 180°

3p + 2p = 180°

5p = 180

p = 180÷5

p = 36

So,

∠1 = 3p = 3 × 36 = 108°

∠2 = 2p = 2 × 36 = 72°

Also,

∠1 = ∠5 = 108°[Pair of corresponding angles]

∠2 = ∠4 = 72° [V•O•A]

∠4 = ∠8 = 72° [Pair of corresponding angles]

∠2 = ∠6 = 72° [Pair of corresponding angles]

∠1 = ∠3 = 108° [V•O•A]

∠3 = ∠7 = 108° [Pair of corresponding angles]

Therefore

∠1 = ∠3 = ∠7 = ∠5 = 108°

∠2 = ∠4 = ∠8 = ∠6 = 72°