Question

determine the value of x.
figure is not drawn to scale
question 3 of 6
angular module 5 assessment
your answer

Explanation:

Step1: Find the measure of ∠KML

Use the linear - pair property. If ∠NMK = 117°, then ∠KML=180° - 117° = 63°.

Step2: Apply the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
For triangle \(KML\), the exterior - angle theorem gives: \(6x - 14=63 + 47\).

Step3: Solve the equation for \(x\)

First, simplify the right - hand side of the equation: \(63+47 = 110\).
So, the equation becomes \(6x-14 = 110\).
Add 14 to both sides: \(6x=110 + 14\), which simplifies to \(6x=124\).
Divide both sides by 6: \(x=\frac{124}{6}=\frac{62}{3}\approx20.67\).

Answer:

\(x = \frac{62}{3}\)