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Find the measure of each angle of a parallelogram, if one of i

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Find the measure of each angle of a parallelogram, if one of its angle is $30^{o}$ less than twice the smallest angle.

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Find the measure of each angle of a parallelogram, if one of its angle is

30^{o}

less than twice the smallest angle.

7 mins ago

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7 mins ago

Text solutionVerified

Consider

A BC D

as a parallelogram

Let us take

∠ A

as the smallest angle

so we get

∠ B = 2∠ A - 30^{o}

we know that the opposite angles are equal in a parallelogram

∠ A = ∠ C

and

∠ B = ∠ D = 2∠ A - 30^{o}

we know that the sum of all the angles of a parallelogram is

360^{o}

it can be written as

∠ A + ∠ B + ∠ C + ∠ D = 360^{o}

by substituting the values in the above equation

∠ A + (2∠ A - 30^{o}) + ∠ A + (2∠ A - 30^{o}) = 360^{o}

6∠ A - 60^{o}

6∠ A = 360^{o} + 60^{o}

∠ A = 70^{o}

by substituting the value of

∠ A

∠ A = ∠ C = 70^{o}

∠ B = ∠ D = 2∠ A - 30^{o} = 2 (70^{o}) - 30^{o}

∠ B = ∠ D = 110^{o}

therefore

∠ A = ∠ C = 70^{o}

and

∠ B = ∠ D = 110^{o}

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Question Text	Find the measure of each angle of a parallelogram, if one of its angle is $30^{o}$ less than twice the smallest angle.
Answer Type	Text solution:1
Upvotes	150