Question

what is the value of k?

Explanation:

Step1: Use the exterior angle theorem

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

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(k\)

Subtract 15 from both sides of the equation: \(10k+15-15=115 - 15\), so \(10k=100\). Then divide both sides by 10: \(k=\frac{100}{10}\).

Answer:

\(10\)