Question

what is the value of k?

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
Here, the exterior angle is \(115^{\circ}\), and the two non - adjacent interior angles are \((4k + 5)^{\circ}\) and \((6k+10)^{\circ}\). So, we can write the equation:
\(4k + 5+6k + 10=115\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\((4k+6k)+(5 + 10)=115\)
\(10k+15 = 115\)

Step3: Solve for \(k\)

Subtract \(15\) from both sides of the equation:
\(10k+15-15=115 - 15\)
\(10k=100\)
Divide both sides by \(10\):
\(k=\frac{100}{10}\)

Answer:

\(10\)