Question

find x and y in the figure given above ​

Answer 1

Answer:

x= 52 and y= 60.....................

Answer 2

Given :-

In ∆ABC , DE || BC.

∠AED = X°

∠ DAE = Y°

∠ABC = 68°

∠EDC = 27°

∠ECD = 25°

Solution :-

Since A-E-C is a Straight Line ,,

So,

→ ∠AED + ∠DEC = 180° (Linear Pair) .

→ x + ∠DEC = 180°

→ ∠DEC = (180° - x) ---------- Equation (1).

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Now, in ∆DEC, we have :-

→ ∠EDC = 27°

→ ∠ECD = 25°

→ ∠DEC = (180° - x) (From Equation (1) )

we know That, Sum of All angles of a ∆ are 180° .

So,

→ ∠EDC + ∠ECD + ∠DEC = 180°

→ 27° + 25° + (180-x)° = 180°

→ 27° + 25° = 180° - 180° + x

→ x = 27° + 25°

→ x = 52° (Ans).

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Now in ∆ADE , we Have :-

→ ∠ADE + ∠DAE + ∠DEA = 180° (By Angle - sum Property).

Now, Given That, DE || BC ,

Hence,

→ ∠ADE = ∠ABC = 68°

→ ∠ADE = 68°

So,

→ ∠ADE + ∠DAE + ∠DEA = 180°

→ 68° + y° + x° = 180°

Putting value of x now, we get,

→ 68° + y° + 52° = 180°

→ y° = 180° - (68° + 52°)

→ y° = 180° - 120°

→ y° = 60° . (Ans).

Hence, value of ∠x is 52° and ∠y is Equal to 60°..

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