Question
Two angles of a quadrilateral are each of measure 75∘ and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
Two angles of a quadrilateral are each of measure 75∘ and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
Answer:
:
Let ABCD be a quadrilateral,
where ∠A=∠C=75∘ and ∠B=∠D=x [say]
Then, by the angle sum property of a quadrilateral, we have
∠A+∠B+∠C+∠D=360∘⇒75∘+x+75∘+x=360∘⇒2x=360∘−150∘⇒2x=210∘⇒x=105∘
Thus, other two angles are of 105∘ each.
Since, opposite angles are equal, therefore the quadrilateral is a parallelogram.
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:
Let ABCD be a quadrilateral,
where ∠A=∠C=75∘ and ∠B=∠D=x [say]
Then, by the angle sum property of a quadrilateral, we have
∠A+∠B+∠C+∠D=360∘⇒75∘+x+75∘+x=360∘⇒2x=360∘−150∘⇒2x=210∘⇒x=105∘
Thus, other two angles are of 105∘ each.
Since, opposite angles are equal, therefore the quadrilateral is a parallelogram.
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