Answer:
Value of k = 10
Step-by-step explanation:
Exterior angle property states that the exterior angle is equal to the sum of the opposite sides of an interior angle.
As per the diagram:
In triangle XZY:
[tex]\angle XZY = (4k+5)^{\circ}[/tex], [tex]\angle ZXY = (6k+10)^{\circ}[/tex] and [tex]\angle ZYM = 115^{\circ}[/tex]
By definition of exterior angle property we have;
[tex]\angle XZY+\angle ZXY = \angle ZYM[/tex]
Substitute the values and solve for k.
[tex]4k+5+6k+10 = 115[/tex]
Combine like terms;
[tex]10k+15 = 115[/tex]
Subtract 15 from both sides we have;
[tex]10k = 100[/tex]
Divide both sides by 10 we have;
k = 10
Therefore, the value of k is, 10
