Question

quadrilateral mntu below is a parallelogram. if ( mangle m = 4x + 6 ) and ( mangle n = 2x + 30 ), what is the value of ( x )?
select the best answer from the choices provided.
a. 12
b. 24
c. 78
d. 102

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary, so \(m\angle M + m\angle N=180^{\circ}\).
Substitute \(m\angle M = 4x + 6\) and \(m\angle N=2x + 30\) into the equation: \((4x + 6)+(2x + 30)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+2x+6 + 30=180\), which gives \(6x+36 = 180\).

Step3: Solve for \(x\)

Subtract 36 from both sides: \(6x=180 - 36\), so \(6x=144\).
Divide both sides by 6: \(x=\frac{144}{6}\).

Answer:

A. 12