Question

Solving for Angle Measures
What is the value of k?

Answer 1

k = 10 degrees

hope this helps!

Answer 2

Value of k = 10

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:

`\angle XZY = (4k+5)^(\circ)`,
`\angle ZXY = (6k+10)^(\circ)` and
`\angle ZYM = 115^(\circ)`

By definition of exterior angle property we have;

`\angle XZY+\angle ZXY = \angle ZYM`

Substitute the values and solve for k.

`4k+5+6k+10 = 115`

Combine like terms;

`10k+15 = 115`

Subtract 15 from both sides we have;

`10k = 100`

Divide both sides by 10 we have;

k = 10

Therefore, the value of k is, 10