Question

1. find ml

jl is labeled 3x + 11, np is labeled 45, ml is labeled 10x - 12. the trapezoid has markings indicating n is the midpoint of jm and p is the midpoint of kl.
ml = type your answer...

Explanation:

Step1: Apply trapezoid midsegment theorem

The midsegment of a trapezoid is equal to half the sum of the two bases, so $\frac{(3x+11)+(10x-12)}{2}=45$.

Step2: Simplify the equation

Combine like terms in the numerator: $\frac{13x - 1}{2}=45$.
Multiply both sides by 2: $13x - 1 = 90$.

Step3: Solve for x

Add 1 to both sides: $13x = 91$.
Divide by 13: $x = \frac{91}{13}=7$.

Step4: Calculate ML

Substitute $x=7$ into $ML=10x-12$: $ML=10(7)-12$.

Answer:

$58$