
How many right angles does a rhombus have?
Answer
536.4k+ views
Hint:
As a parallelogram, the rhombus has a sum of two interior angles that share a side equal to ${180^\circ }$.
Therefore, only if all angles are equal, they all are equal to ${90^ \circ }$.
That equality of all angles makes a square out of a rhombus.
Complete step by step answer:
It can be either $0$ or $4$ but never $1$,$2$ or $3$.
A rhombus is a Parallelogram with $4$ equal sides. Because it is a parallelogram, opposite angles are congruent. And because it is a quadrilateral the sum of all angles must $ = {360^\circ }$. So if one angle is right then the opposite angle is ${90^ \circ }$. Then the $1st$ pair has a sum of $180$ degrees, then$360 - 180 = 180$
So the other pair of angles sum to ${180^\circ }$ degrees. But the other pair of angles are also opposite of each other so must be congruent, so each of the other two angles is also ${90^ \circ }$ degrees. So if one angle is right all $4$ angles are right angles. These kinds of rhombi, or rhombuses, are called squares. Squares are a subset of rhombi or the rhombus could have no right angles, it would just be a rhombus.
Note:
If a rhombus is a square, all four of its angles are right. Otherwise, all angles are either acute or obtuse, but not right. Also, all sides of rhombus are equal. Typically we say, it's a subpart of a square because all the properties are the same except angle.
As a parallelogram, the rhombus has a sum of two interior angles that share a side equal to ${180^\circ }$.
Therefore, only if all angles are equal, they all are equal to ${90^ \circ }$.
That equality of all angles makes a square out of a rhombus.
Complete step by step answer:
It can be either $0$ or $4$ but never $1$,$2$ or $3$.
A rhombus is a Parallelogram with $4$ equal sides. Because it is a parallelogram, opposite angles are congruent. And because it is a quadrilateral the sum of all angles must $ = {360^\circ }$. So if one angle is right then the opposite angle is ${90^ \circ }$. Then the $1st$ pair has a sum of $180$ degrees, then$360 - 180 = 180$
So the other pair of angles sum to ${180^\circ }$ degrees. But the other pair of angles are also opposite of each other so must be congruent, so each of the other two angles is also ${90^ \circ }$ degrees. So if one angle is right all $4$ angles are right angles. These kinds of rhombi, or rhombuses, are called squares. Squares are a subset of rhombi or the rhombus could have no right angles, it would just be a rhombus.
Note:
If a rhombus is a square, all four of its angles are right. Otherwise, all angles are either acute or obtuse, but not right. Also, all sides of rhombus are equal. Typically we say, it's a subpart of a square because all the properties are the same except angle.
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