What could be the measure of x and y if ABCD is a parallelogram-45-30B- X -45y-35-C- x-40y -30-D- x-40-y -35-

The correct option is A x = 45° y = 30° Since, nbsp;the opposite angles of a parallelogram are equal. ∴ ∠ D = ∠ B ⇒ (x+80)° = (3x 10)° ⇒ 80°+10° = 3x x ⇒ 2 ...

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Byju's Answer

Standard IX

Mathematics

Opposite Angles of a Parallelogram Are Equal

What could be...

Question

What could be the measure of $x$ and $y$ if ABCD is a parallelogram?

x = 45 ° y = 30 °

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x = 40 ° y = 30 °

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x = 45 ° y = 35 °

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x = 40 ° y = 35 °

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Solution

The correct option is A $x = 45 ° y = 30 °$

Since, the opposite angles of a parallelogram are equal.
$∴ ∠ D = ∠ B$
$\Rightarrow (x + 80) ° = (3 x - 10) °$
$\Rightarrow 80 ° + 10 ° = 3 x - x$
$\Rightarrow 2 x = 90 °$
$\Rightarrow x = 45 °$

Also, the sum of the adjacent angles of a parallelogram is 180°.
$∴ ∠ B + ∠ C = 180 °$
$\Rightarrow (3 x - 10) ° + (y + 25) ° = 180 °$
$\Rightarrow ((3 \times 45 °) - 10 °) + (y + 25) ° = 180 ° ...(since, x = 45°)$
$\Rightarrow 135 ° - 10 ° + y + 25 ° = 180 °$
$\Rightarrow y = 180 ° - 150 °$
$\Rightarrow y = 30 °$

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What could be the measure of x and y if ABCD is a parallelogram?

What could be the measure of $x$ and $y$ if ABCD is a parallelogram?