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Geometry 8 Online
OpenStudy (anonymous):

What is the measure of Angle 1? 47o 37o 74o<-- 53o See Attachment

OpenStudy (anonymous):

OpenStudy (phi):

How did you get that ?

OpenStudy (anonymous):

I added 53 degrees as x and put them in the equations and decided it was 74 degrees .. I think i'm very wrong.

OpenStudy (phi):

Do we know if the figure is a parallelogram or rhombus ?

OpenStudy (anonymous):

It is a rhombus

OpenStudy (phi):

In that case, according to wikipedia A simple (non self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following: a quadrilateral with four sides of equal length (by definition) a quadrilateral in which the diagonals are perpendicular and bisect each other a quadrilateral in which each diagonal bisects two opposite interior angles a parallelogram in which at least two consecutive sides are equal in length a parallelogram in which the diagonals are perpendicular a parallelogram in which a diagonal bisects an interior angle notice that last property.

OpenStudy (anonymous):

I know it's a rhombus it says that it is.

OpenStudy (anonymous):

I'm just wondering if i'm right or if i'm wrong where I went wrong.

OpenStudy (phi):

When you have a rhombus, then you know its diagonals bisect the angles.

OpenStudy (anonymous):

Oh my gosh it was right in front of my face angle 1 is 53 -.- sorry

OpenStudy (phi):

QS is a diagonal and it bisects angle RST

OpenStudy (phi):

you could also have used congruent triangles to figure it out. triangle STQ is congruent to triangle QRS by side-side-side. that will make angle 1 equal to 53º

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