Question

solving for angle measures
what is the value of k?
115°
(4k + 5)°
(6k + 10)°

Explanation:

Step1: Apply 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, \(115^{\circ}=(4k + 5)^{\circ}+(6k + 10)^{\circ}\).

Step2: Simplify the equation

$$
LATEXBLOCK0
$$

Step3: Solve for \(k\)

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

Answer:

\(10\)