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Answer :
Final answer:
The value of angle klm, given that angles klm and pqr are complementary and represented by the expressions 4x - 3 and x + 13 respectively, is found to be 61 degrees.
Explanation:
In geometry, two angles are said to be complementary if the sum of their measures is 90 degrees. In this case, angle klm and angle pqr are stated to be complementary, meaning together they add up to 90 degrees. Therefore, we can set up an equation based on the given expressions for these two angles:
4x-3 + x+ 13 = 90
Make a simplification by summing up like terms:
5x + 10 = 90
You can now solve this linear equation for the variable x by subtracting 10 from both sides to get 5x = 80, then dividing both sides by 5 to get x = 16. With x now known, you can substitute 16 in to the expression for angle klm to get its measure:
Angle klm = 4x - 3 = 4(16) - 3 = 64 - 3 = 61 degrees
So, the value of angle klm is 61 degrees.
Learn more about Complementary angles
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