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Answer :
Final answer:
The value of x is found using the exterior angle theorem. Simplifying the resulting equation gives us x = 11.
Explanation:
In the triangle AKLM with the extended line KM to point N, we can use the concept of exterior angles to find the value of x. The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Given that the measure of angle MKL (m∠MKL) is (3x + 19)° while that of angle KLM (m∠KLM) is (2x + 8)°, we can write the exterior angle LMN (m∠LMN) as the sum of these two angles: (3x + 19)° + (2x + 8)° = (7x + 5)°. This leads to a simple equation: 5x + 27 = 7x + 5.
Our calculation steps proceed by first simplifying this equation: subtracting 5x from both sides gives us 27 = 2x + 5. Then, subtracting 5 from both sides gives us 22 = 2x, and finally, dividing both sides by 2 yields x = 11.
Learn more about Exterior Angle Theorem here:
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