Question

lmno is a parallelogram, with \\( \angle m = (11x) ^ { \circ } \\) and \\( \angle n = (6x - 7) ^ { \circ } \\). which statements are true about parallelogram lmno? choose three correct answers.
\\( m \angle m = 111 ^ { \circ } \\)
\\( m \angle n = 59 ^ { \circ } \\)
\\( m \angle o = 121 ^ { \circ } \\)
\\( m \angle l = 22 ^ { \circ } \\)
\\( x = 11 \\)

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 \(m\angle M=(11x)^{\circ}\) and \(m\angle N=(6x - 7)^{\circ}\) into the equation:
\(11x+(6x - 7)=180\)
\(11x+6x-7 = 180\)
\(17x=180 + 7\)
\(17x=187\)
\(x = 11\)

Step2: Calculate the measure of \(\angle M\)

Substitute \(x = 11\) into \(m\angle M=(11x)^{\circ}\):
\(m\angle M=11\times11=121^{\circ}\)

Step3: Calculate the measure of \(\angle N\)

Substitute \(x = 11\) into \(m\angle N=(6x - 7)^{\circ}\):
\(m\angle N=6\times11-7=66 - 7=59^{\circ}\)

Step4: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So, \(m\angle O=m\angle M = 121^{\circ}\) and \(m\angle L=m\angle N=59^{\circ}\)

Answer:

\(m\angle N = 59^{\circ}\), \(m\angle O = 121^{\circ}\), \(x = 11\)