Question 3:
Since, EG = EF + FG
[tex]64 = 2x-2+3x+1[/tex]
[tex]64 = 5x -1[/tex]
[tex]65 = 5x[/tex]
x = 13
So, EF = [tex]2x-2[/tex]
= [tex](2 \times 13)-2 = 26-2=24[/tex]
So, EF = 24 units.
Question 4:
Since, [tex]XY \cong YZ[/tex]
So, [tex]XY = YZ[/tex]
[tex]9x-7 = 3x+5[/tex]
[tex]6x = 12[/tex]
So, x =2
Question 5:
Since, [tex]XY \cong YZ[/tex]
By being congruent, the measures of the segments are equal.
So, [tex]9x-7 = 3x+5[/tex]
[tex]9x - 3x = 12[/tex]
[tex]6x = 12[/tex]
So, x = 2
Now, XZ = [tex]XY + YZ[/tex]
XY = 9x - 7 = [tex](9 \times 2) - 7 = 11[/tex]
YZ = 3x + 5 [tex]= (3 \times 2) + 5 = 11[/tex]
XZ = XY + YZ = 11 + 11 = 22 units.
Question 6:
It is given that [tex]m \angle ABC \cong m \angle DBE[/tex]
It means that the measures of these two angles are equal.
Since, measure of angle ABC is 35 degrees.
Therefore, the measure of angle DBE is 35 degrees.
