Question

lmno is a parallelogram, with \\( \angle m = ( 1 1 x ) ^ { \circ } \\) and \\( \angle n = ( 6 x - 7 ) ^ { \circ } \\). which statements are true about parallelogram lmno? select three options. \\( \square x = 11 \\) \\( \square m \angle l = 22 ^ { \circ } \\) \\( \square m \angle m = 111 ^ { \circ } \\) \\( \square m \angle n = 59 ^ { \circ } \\) \\( \square m \angle o = 121 ^ { \circ } \\)

Explanation:

Step1: Use property of parallelogram adjacent angles

In a parallelogram, adjacent angles are supplementary. So, \(\angle M+\angle N = 180^{\circ}\).
Substitute \(\angle M=(11x)^{\circ}\) and \(\angle N=(6x - 7)^{\circ}\) into the equation:
\(11x+(6x - 7)=180\)
\(11x+6x-7 = 180\)
\(17x=180 + 7\)
\(17x=187\)
\(x=\frac{187}{17}=11\)

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

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

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

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

Step4: Use property of parallelogram opposite angles

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

Answer:

A. \(x = 11\)
D. \(m\angle N=59^{\circ}\)
E. \(m\angle O = 121^{\circ}\)