Question

question
in \\( \delta k l m, \mathrm { m } \angle k = ( 4 x - 3 ) ^ { \circ }, \mathrm { m } \angle l = ( x - 8 ) ^ { \circ }, \\) and \\( \mathrm { m } \angle m = ( 5 x + 1 ) ^ { \circ } \\). what is the value of \\( x? \\)

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle K+m\angle L + m\angle M=180^{\circ}\).
Substitute the given angle expressions: \((4x - 3)+(x - 8)+(5x + 1)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((4x+x + 5x)+(-3-8 + 1)=180\).
\(10x-10 = 180\).

Step3: Solve for \(x\)

Add \(10\) to both sides of the equation: \(10x-10 + 10=180 + 10\).
\(10x=190\).
Divide both sides by \(10\): \(x=\frac{190}{10}=19\).

Answer:

\(x = 19\)