Question

I have already answer but want explanation

help me

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Answer 1

Answer:

∠x = 45°

∠y = 95°

∠z = 40°

Step-by-step explanation:

clearly ∠x,∠y and ∠z are the angles on a straight line, AB

=> ∠x+∠y+∠z = 180°  ------------ (1)

let us assume the 3rd vertex of the triangle be C (not given in diagram)

=> in triangle, CDE, ∠C+∠D+∠E = 180°

given that ∠C = ∠y and ∠D=45° and ∠E=40°

=>  ∠y+45°+40° = 180°

=> ∠y +85° = 180°

=> ∠y = 180° - 85°

=> ∠y = 95°

Now ,

It is also given that AB ║ DE

if taken CD as the transversal , then

we have ∠ACD & ∠CDE are interior alternate angles and so they are equal

=> ∠ACD = ∠CDE

=> ∠x  = 45°

similarly, if CE is taken the transversal, then

we have ∠BCE & ∠CED are interior alternate angles and so they are equal

=> ∠BCE = ∠CED

=> ∠z  = 40°

and so, we have the solutions

∠x = 45°

∠y = 95°

∠z = 40°

Answer 2

Answer:

$∠u = 45° \:(alternate \: angle)$

$∠z = 40°(alternate \: angle)$

$∠u + ∠y + ∠z = 180°(angle \: sum \: property \: of \: a \: triangle)$

$45° + ∠ y+ 40° = 180°$

$∠y + 85° = 180°$

$∠y = 180° - 85°$

$∠y = 95°$

Therefore value of

Therefore value of ∠u = 45°

Therefore value of ∠u = 45°∠y = 40°

Therefore value of ∠u = 45°∠y = 40°∠z = 95°