Question

in the given figure, AB ll PQ. find the value of x and y .
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Answer 1

${\sf{\underline{\underline{\pink{Solution:-}}}}}$

${\sf{\underline{\blue{Given:-}}}}$

• AB || PQ and EF is a transversal.

From the figure we know that ∠CEB and ∠EFQ are corresponding angles.

$\sf\green{So \ we \ get}$

• ∠CEB = ∠EFQ = 75°

$\sf\orange{It \ can \ be \ written \ as}$

• ∠EFQ = 75°

$\sf\red{Where}$

• ∠EFG + ∠GFQ = 75°

$\sf\purple{By \ substituting \ the \ values}$

• 25o + yo = 75°

$\sf\pink{ On \ further \ calculation}$

• y°= 75o – 25°

$\sf\orange{ By \ subtraction}$

• yo = 50°

From the figure we know that ∠BEF and ∠EFQ are consecutive interior angles

$\sf\orange{ So \ we \ get}$

• ∠BEF + ∠EFQ = 180°

$\sf\pink{ By \ substituting \ the \ values}$

• ∠BEF + 75° = 180°

$\sf\green{On \ further \ calculation}$

• ∠BEF = 180° – 75°

$\sf\orange{ By \ subtraction}$

• ∠BEF = 105°

We know that ∠BEF can be written as

• ∠BEF = ∠FEG + ∠GEB

• 105° = ∠FEG + 20°

$\sf\orange{ On \ further \ calculation}$

∠FEG = 105°– 20°

$\sf\pink{ By \ subtraction}$

• ∠FEG = 85°

According to the △ EFG

$\sf\red{ We \ can \ write}$

• x° + 25° + ∠FEG = 180°

$\sf\green{ By \ substituting \ the \ values}$

• x° + 25° + 85° = 180°

$\sf\purple{ On \ further \ calculation}$

• x° = 180° – 25° – 85°

$\sf\pink{ By \ subtraction}$

• x° = 180°– 110°
• x° = 70°

Therefore, the value of x is 70.