Question

PLeAsE i NeEd HeLp!!!!

Answer 1

Answer:

DF = 10 units

$m\angle DFG = 28^\circ$

EG = 5.04

Step-by-step explanation:

Properties of Rhombus es

1. All Sides Of The Rhombus Are Equal.
2. The Opposite Sides Of A Rhombus Are Parallel.
3. Opposite Angles Of A Rhombus Are Equal.
4. In A Rhombus, Diagonals Bisect Each Other At Right Angles.
5. Diagonals Bisect The Angles Of A Rhombus.

The image contains a rhombus with the following data (assume the center as point O):

DO = 5 units

GF = 5.6 units

$m\angle FEO = 62^\circ$

4. Calculate DF

Applying property 4, diagonals bisect each other, thus the length of DF is double the length of DO, i.e. DF=2*5 = 10:

DF = 10 units

5. Calculate $m\angle DFG$

Applying property 4 in triangle EFO, the center angle is 90°, thus angle EFO has a measure of 90°-62°=28°.

Applying property 5, this angle is half of the measure of angle EFG and angle DFG has the same measure of 28°.

$m\angle DFG = 28^\circ$

6. FG is the hypotenuse of triangle OFG, thus:

$OG^2=FG^2-OF^2$

$OG^2=5.6^2-5^2$

$OG^2=6.36$

$OG=\sqrt{6.36}=2.52$

EG is double OG: OG=2*2.52=5.04

EG = 5.04