a. Solve for x
Since angle MLN and angle JKL are complementary, the value of x = 8
Since angle MLN and angle JKL are complementary, their sum equal 90°.
Since angle MLN = 7x - 1 and angle JKL = 4x + 3, we have that
7x - 1 + 4x + 3 = 90
Collecting like terms, we have
7x + 4x - 1 + 3 = 90
Simplifying, we have
11x + 2 = 90
Subtracting 2 from both sides, we have
11x = 90 - 2
11x = 88
Dividing through by 11, we have
x = 88/11
x = 8
So, Since angle MLN and angle JKL are complementary, the value of x = 8
b. Find m angle MLN and m angle JKL .
Since angle MLN=7x-1 and angle JLK=4x+3 thus, angle MLN = 55° and angle JKL = 35°
Since angle MLN = 7x - 1 and x = 8, we have
angle MLN = 7x - 1
angle MLN = 7(8) - 1
angle MLN = 56 - 1
angle MLN = 55°
Since angle JKL = 4x + 3 and x = 8, we have
angle JKL = 4x + 3
angle JKL = 4(8) + 3
angle JKL = 32 + 3
angle JKL = 35°
So, Since angle MLN=7x-1 and angle JLK=4x+3 thus, angle MLN = 55° and angle JKL = 35°
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