Math, asked by shubhamseth26026, 1 year ago

if m।। n and p and q are the transversel find angel 5 and angel 3... see the figure

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Answered by AparajitaDas

hi there,

Given: ∠1 = 123° , ∠4 = 85° To find : ∠2, ∠3,∠5, ∠6

Proof:
∠1 = ∠2 = 123° (Alternate interior angles)

∠3 + ∠2 = 180 ° (Linear Pair)
∠3 = 180 - ∠2
= 180 - 123
= 57°

∠4 + ∠6 = 180 (Linear Pair)
∠6 = 180 - ∠4
= 180 - 85
= 95°

∠5 = ∠6 (Vertically Opposite Angles....same as ∠1 and ∠2 given above)

Hope this helps

ChirikaSasaki: A mistake is there.

AparajitaDas: May i know the mistake ?

ChirikaSasaki: sure.

ChirikaSasaki: angle 1&2 is not vertically opposite angles. They are pairs of interior alternate angles.

ChirikaSasaki: meant to say angles 1&2

ChirikaSasaki: angles 1 & 2

AparajitaDas: well i am glad you pointed that....but isn't my solution correct

ChirikaSasaki: of course your solution is correct. But the way of reasoning is wrong.

AparajitaDas: thank you ...i will pay more attention from next time

ChirikaSasaki: That's fine. Follow and thank my answer.

Answered by ChirikaSasaki

Here, angle 1=angle 2=123degrees [pairs of interior alternate angles].
then, we have angle 2 + 3= 180degrees. [they form supplementary angle. ]
=> 123 + angle 3= 180
=> angle 3= 180 - 123.
therefore, angle 3=57degrees.
Again, angle 4 + 6 = 180
=> 85 + angle 6 = 180
=> angle 6 = 180- 85
=> angle 6 = 95degrees.
then, angle 6 = 5 = 95degrees [pairs of exterior alternate angles].

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