Brenda H.

asked • 01/28/16

PQRS is a Rhombus. m<PQS = (3x=10) and m<SQR = (x=40) Find m<QRS

 What is the measure of M<QRS?

Yohan C.

Brenda,
 
is it really m<PQS = (3x = 10)? not (3x+10)?
 
and
 
are you saying that measure of SQR = 40 degrees?
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01/29/16

Yohan C.

Remember, here are the characteristics for rhombus:
 
1.  All sides are equal/congruent
2.  Opposite sides are equal/congruent
3.  Opposite sides are parallel
4.  Opposite angles are equal/congruent
5.  All internal angles add up to 360 degrees
6.  the diagonals are perpendicular
7.  the diagonals bisect each other
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01/29/16

1 Expert Answer

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Yohan C. answered • 01/29/16

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If you are saying measure of angle SQR = 40 degrees, then here is how to get QRS:
 
Apply 6 & 7 from my Comment.  That will give you <Q = 80 degrees.  This will determine  <S = 80 degrees because opposite angles are equal/congruent.  Sum of those 2 angles will give you 160 degrees. 
 
So, remaining 2 angles (P & R) must be add up to 200 degrees to make 360 degrees.  And they must be equal.  Therefore each of <P and <R are 100 degrees each.  So, your angle <QRS (same as <R) is 100 degrees.
 
I hope you understood.  Good luck to you.
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