Question

do it fast...........​

Answer 1

${ \frak { \underline \purple{Correct \: Question : - }}} \:$

One angle of a parallelogram is 45° more than its adjacent angle. Find the angles of the parallelogram.

${ \frak { \underline \purple{Required \: Answer : - }}} \:$

${ \frak { \underline \purple{Given : - }}} \:$

One angle of parallelogram is 45° more than its adjacent angle.

${ \frak { \underline \purple{To \: Find : - }}} \:$

All angles of given parallelogram.

$\large\boxed{\boxed{\sf{ ⇝So\:let's \:do\:it\::-}}}$

Let it's adjacent angle of given angle = x

Atq,

ㅤㅤGiven angle is 45° more than it's ㅤㅤㅤㅤadjacent angle.

∴ Given angle = x + 45°

Now,

Sum of adjacent angles of llgm = 180°

So,

ㅤx + x + 45° = 180°

ㅤ2x + 45° = 180°

ㅤ2x = 180° - 45°

ㅤ2x = 135°

ㅤx = $\dfrac{135°}{2}$

ㅤx = $\cancel{\dfrac{135°}{2}}$

ㅤx = 67.5°

∴ Adjacent angle of given angle = 67.5°

$\sf{So, \:Given \:angle\: = x \:+ \:45°\: =\: 67.5°\: +\: 45° \:=\: \boxed{112.5°}}$

Opposite angles of llgm are equal

∴ ∠A = ∠C = 112.5°

ㅤ∠B = ∠D = 67.5°

★ Diagram is in the attachment ★

$\huge\mathrm{\underline \green {Hence\:Solved}}$

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Answer 2

Answer:

${ \frak { \underline \purple{Correct \: Question : - }}} \:$

One angle of a parallelogram is 45° more than its adjacent angle. Find the angles of the parallelogram.

${ \frak { \underline \purple{Required \: Answer : - }}} \:$

${ \frak { \underline \purple{Given : - }}} \:$

One angle of parallelogram is 45° more than its adjacent angle.

${ \frak { \underline \purple{To \: Find : - }}} \:$

All angles of given parallelogram.

$\large\boxed{\boxed{\sf{ ⇝So\:let's \:do\:it\::-}}}$

Let it's adjacent angle of given angle = x

Atq,

ㅤㅤGiven angle is 45° more than it's ㅤㅤㅤㅤadjacent angle.

∴ Given angle = x + 45°

Now,

Sum of adjacent angles of llgm = 180°

So,

ㅤx + x + 45° = 180°

ㅤ2x + 45° = 180°

ㅤ2x = 180° - 45°

ㅤ2x = 135°

ㅤx = $\dfrac{135°}{2}$

ㅤx = $\cancel{\dfrac{135°}{2}}$

ㅤx = 67.5°

∴ Adjacent angle of given angle = 67.5°

$\sf{So, \:Given \:angle\: = x \:+ \:45°\: =\: 67.5°\: +\: 45° \:=\: \boxed{112.5°}}$

Opposite angles of llgm are equal

∴ ∠A = ∠C = 112.5°

ㅤ∠B = ∠D = 67.5°

★ Diagram is in the attachment ★

$\huge\mathrm{\underline \green {Hence\:Solved}}$

_________________________________________________________