Question

what is the value of k? diagram: points l, z, y, m, x, n with angles 115°, (4k + 5)°, (6k + 10)°

Explanation:

Step1: Identify exterior angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, \(115^{\circ}\) is an exterior angle, and \((4k + 5)^{\circ}\) and \((6k+10)^{\circ}\) are the two non - adjacent interior angles. 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.
\((4k+6k)+(5 + 10)=115\)
\(10k+15 = 115\)

Step3: Solve for k

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

Answer:

\(10\)