Question

what is the value of k? 115° at y, (4k + 5)° at z, (6k + 10)° at x, with lines and points l, z, x, n and m, y.

Explanation:

Step1: Identify exterior angle property

The exterior angle of a triangle equals the sum of the two non - adjacent interior angles. Here, the exterior angle at Y is \(115^{\circ}\), and the two non - adjacent interior angles are \((4k + 5)^{\circ}\) and \((6k+10)^{\circ}\). So we can set up the equation: \(4k + 5+6k + 10=115\).

Step2: Combine like terms

Combine the \(k\) terms and the constant terms on the left - hand side of the equation. \(4k+6k=10k\) and \(5 + 10 = 15\). So the equation becomes \(10k+15 = 115\).

Step3: Solve for k

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

Answer:

\(10\)