Answer:
the value of y is, 5.5
Explanation:
GIven: [tex]m\angle KLM=135^{\circ}[/tex]
Linear pairs is a pair of adjacent angles formed when two lines intersect.
In the figure, [tex]m\angle kLN[/tex] and [tex]m\angle MLN[/tex] forms a linear pair.
then, [tex]m\angle KLM = m\angle KLN+m\angle MLN[/tex].
Substitute the values of [tex]m\angle KLN= 47^{\circ}[/tex] and [tex]m\angle MLN= (16y)^{\circ}[/tex] in above equation, to find the value of y;
⇒ [tex]135^{\circ}=47^{\circ}+(16y)^{\circ}[/tex] or
[tex]16y^{\circ} =135^{\circ}-47^{\circ}[/tex]
Simplify:
[tex]16y^{\circ} =88[/tex]
Divide 16 on both sides of an equation:
[tex]\frac{16y}{16} =\frac{88}{16}[/tex]
Simplify:
[tex]y=\frac{11}{2}[/tex] or y=5.5
Therefore, the value of y =[tex]\frac{11}{2}[/tex] or y=5.5.
