Question

ving for angle measures
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, \(115^{\circ}=(4k + 5)^{\circ}+(6k + 10)^{\circ}\)

Step2: Simplify the equation

Combine like terms:

$$
LATEXBLOCK0
$$

Step3: Solve for \(k\)

Subtract \(15\) from both sides of the equation:

$$
LATEXBLOCK1
$$

Divide both sides by \(10\):

$$k=\frac{100}{10}=10$$

Answer:

\(10\)