In a parallelogram ABCD find the measure of all the angles if one its angles is 15° less than twice the smallest angle.
Answers
Answer:
parallelogram ABCD,
Let ∠A be x. Then, ∠B will be 2x−15
o
We know that, in a parallelogram sum of adjacent angles are supplementary.
∴ ∠A+∠B=180
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⇒ x+2x−15
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=180
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⇒ 3x=195
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⇒ x=65
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.
∴ ∠A=65
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⇒ ∠B=2x−15
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=2×65
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−15
o
=115
o
.
We know that, in parallelogram opposite angles are equal.
∴ ∠A=∠C and ∠B=∠D
∴ ∠C=65
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and ∠D=115
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.
∴ The measure of all angles of a parallelogram are 65
o
,115
o
,65
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and 115
o
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