Question

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

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

Step2: Simplify the equation

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

Step3: Solve for \(k\)

Subtract 15 from both sides: \(115-15=10k+15 - 15\).
\(100 = 10k\).
Divide both sides by 10: \(\frac{100}{10}=\frac{10k}{10}\).

Answer:

\(10\)