Question

given that the quadrilateral lmno is a parallelogram, ( mangle l = 15x + 10 ) and ( mangle m = 4x + 18 ) what is ( mangle l )?

( mangle l=)______
( circ )

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. So, \(m\angle L + m\angle M=180^{\circ}\).
Substitute \(m\angle L = 15x + 10\) and \(m\angle M = 4x + 18\) into the equation:
\((15x + 10)+(4x + 18)=180\)

Step2: Simplify the equation

Combine like - terms:
\(15x+4x+10 + 18=180\)
\(19x+28 = 180\)
Subtract 28 from both sides:
\(19x=180 - 28\)
\(19x=152\)
Divide both sides by 19:
\(x=\frac{152}{19}=8\)

Step3: Find \(m\angle L\)

Substitute \(x = 8\) into \(m\angle L=15x + 10\)
\(m\angle L=15\times8+10\)
\(m\angle L=120 + 10\)
\(m\angle L=130\)

Answer:

\(130\)