solving for angle measures\nwhat is the value of k?\n115°\n(4k + 5)°\n(6k + 10)°

Answer

Explanation:

Step1: Use the exterior - angle property of a triangle

The exterior - angle of a triangle is equal to 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 write 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), which simplifies to (10k+15 = 115).

Step3: Isolate the variable term

Subtract 15 from both sides of the equation: (10k+15−15=115 - 15), resulting in (10k=100).

Step4: Solve for (k)

Divide both sides of the equation by 10: (\frac{10k}{10}=\frac{100}{10}), so (k = 10).