RHOMBUS
》an example of a quadrilateral polygon
》four sides are all equal
》four angles are all equal
》no angles are exactly 90°
》another form of a square
QUESTION
Find the indicated measure of Rhombus EFGH where I is the vertex centroid.
ANSWER
3. m∠FGE = 35°
4. m∠FEI = 20°
5. m∠IFE = 60°
6. m∠IEH = 32°
7. m∠IGH + m∠HIG = 115°
SOLUTION
3. If m∠HGE = 35, find m∠FGE
Since it is a shape wherein all sides are equal, the angles of it will be exactly cut in half. In other words, m∠HGE will be equal to m∠FGE, m∠HGE = m∠FGE.
Hence,
m∠FGE = 35°
4. If m∠HEI = 20, find m∠FEI
The only difference of this is that the other end of the angle ends in a vertex centroid but it is exactly the same as number 3.
Hence,
m∠FEI = 20°
5. If m∠IEF = 30, find m∠IFE
We can see that IFE forms a triangle which is equal to 180° when combining all of its angles and it is a rhombus, thus, m∠FIE, or the vertex centroid is a right angle or the same as a 90°.
Hence,
m∠IEF + m∠IFE + m∠FIE = 180
30 + m∠IFE + 90 = 180
m∠IFE + 120 = 180
m∠IFE + 120 - 120 = 180 - 120
m∠IFE = 60°
6. If m∠IHE = 58, find m∠IEH
This is jus exactly the same as number 4.
Hence,
m∠IHE + m∠IEH + m∠HIE = 180
58 + m∠IEH + 90 = 180
m∠IEH + 148 = 180
m∠IEH + 148 - 148 = 180 - 148
m∠IEH = 32°
7. If m∠IGH = 25, find m∠IGH + m∠HIG
m∠IGH is already given, and we know the all vertex centroid of a rhombus is a right triangle which is equal to 90°.
Hence,
m∠IGH + m∠HIG
= 25 + 90
= 115°
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