Question

PLeAsE i NeEd HeLp!!!!

Answer 1

DF = 10 units

`m\angle DFG = 28^\circ`

EG = 5.04

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=√(6.36)=2.52`

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

EG = 5.04