Answer with Step-by-step explanation:
We are given that
1.TV=a=95.2 cm
VY=x'=34 cm
TK=b=168cm
Angle bisector theorem:it states that an angle bisector divides the opposite side in such a way that the ratio of segments formed after bisection is equal to ratio of other two sides.
By angle bisector theorem
[tex]\frac{a}{x}=\frac{b}{y}[/tex]
[tex]\frac{TV}{VY}=\frac{TK}{YK}[/tex]
[tex]\frac{95.2}{34}=\frac{168}{YK}[/tex]
[tex]YK=\farc{168\times 34}{95.2}=60 cm[/tex]
Value of x=VK=VY+YK=34+60=94 cm
2.Triangle proportionality theorem: When a line is drawn parallel to one side then it intersect other two sides and it will divides the other two side proportionally.
[tex]\frac{AN}{MN}=\frac{BP}{MP}[/tex] By triangle proportionality theorem
Substitute the values then we get
[tex]\frac{22}{71.5}=\frac{BP}{97.5}[/tex]
[tex]BP=\frac{22\times 97.5}{71.5}=30 cm[/tex]
[tex]MB=x=MP-BP=97.5-30=67.5 cm[/tex]
3.[tex]\frac{EG}{GD}=\frac{EH}{HD}[/tex] By triangle proportionality theorem
Substitute the values then we get
[tex]\frac{44.8}{x+4}=\frac{56}{35}[/tex]
[tex]x+4=\frac{44.8\times 35}{56}=28[/tex]
[tex]x=28-4=24 mm[/tex]
4.[tex]\frac{5}{40}=\frac{3}{2x+10}[/tex]
By triangle proportionality theorem
[tex]2x+10=\frac{3\times 40}{5}=24[/tex]
[tex]2x=24-10=14[/tex]
[tex]x=\frac{14}{2}=7 cm[/tex]
