Question

In fig. ABCD is a parallelogram. Find the value of x and y.​

Answer 1

$\huge\rm { ☆_!! </strong><strong>Qu</strong><strong>estion</strong><strong> !_! ☆}$

In fig. ABCD is a parallelogram. Find the value of x and y.

$\huge\rm { ☆_!! Answer !_! ☆}$

⨳ value of x = 45

⨳ value of y =30

$\huge\rm { ☆_!! Solution !_! ☆}$

$\sf\blue{ ◈ Given - }$

∠ A - ( 3x - 10 ) °

∠ C - ( x + 80 ) °

∠ D - ( y + 25 ) °

$\sf\blue{ ◈ To \: Find - }$

Value of x and y

$\sf\blue{ ◈ Let's \: Solve \: It -}$

∠ A = ∠ C [ † opposite angles of parallelogram are equal ]

↝ ( 3x - 10 ) ° = ( x + 80 ) °

↝ 3x - x = 80 + 10

↝ 2x = 90

↝ x = 90/2

↝ x = 45

So , the value of x is 45

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∠ A + ∠ D = 180 ° [ † sum of adjacent angles of parallelogram is 180° ]

↝ ( 3x - 10 ) ° + ( y + 25 ) ° = 180 °

↝ ( 3 × 45 - 10 ) + ( y + 25 ) = 180

↝ 125 + y + 25 = 180 °

↝ y = 180 - 125 - 25

↝ y = 30

So , the value of y is 30

$\sf\blue{ ◈ Let's \: check -}$ ........ ✍️

↝∠ A = 3 × ( 45 ) - 10 = 125 °

↝∠ C = ( 45 ) + 80 = 125 °

↝∠ D = ( 30 ) + 25 = 55 °

↝∠ B = ∠ D = 55 ° [ † opposite angles of parallelogram are equal]

★ ∠ A + ∠ B + ∠ C + ∠ D = 360°

↝ 125 ° + 125 ° + 55 ° + 55 ° = 360 °

↝ 250 ° + 110 ° = 360 °

↝360 ° = 360 °

hence it is correct !

Answer 2

Answer:

x = 45

y = 30

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