The value of the variable "x" is 11.
We have a triangle. The vertices of the triangle are K, L, and M. The side KM is extended from point M to point N. The measures of the angles MKL, LMN, and KLM are (3x + 19)°, (7x + 5)°, and (2x + 8)°, respectively. We need to find out the value of the variable "x".
The angles LMK and LMN form a linear pair. It means they are supplementary angles. The sum of the angles is 180°.
∠LMK + ∠LMN = 180°
∠LMK + (7x + 5)° = 180°
∠LMK = 180° - (7x + 5)°
In the triangle KLM, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.
∠K + ∠L + ∠M = 180°
(3x +19)° + (2x + 8)° + [180° - (7x + 5)°] = 180°
3x +19 + 2x + 8 + 180 - 7x - 5 = 180
-2x + 22 = 0
2x = 22
x = 11
Hence, the value of the variable "x" is 11.
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