Question

select all of the statements that are true.

□ ( m angle h l d = 127 ^ { circ } )

□ ( angle n l v cong angle d g n )

□ ( angle r d l cong angle y l d )

□ ( angle g l h cong angle x g l )

□ ( angle y l v cong angle d g l )

Explanation:

Step1: Analyze \(m\angle HLD = 127^{\circ}\)

There is no information given in the diagram to calculate or confirm that \(m\angle HLD = 127^{\circ}\). So this statement is not necessarily true.

Step2: Analyze \(\angle NLV\cong\angle DGN\)

\(\angle NLV\) and \(\angle DGN\) are alternate - interior angles. If \(SX\parallel HV\) (assuming the lines are parallel based on the problem's nature of angle - congruence checks), then by the alternate - interior angles theorem, \(\angle NLV\cong\angle DGN\).

Step3: Analyze \(\angle RDL\cong\angle YLD\)

\(\angle RDL\) and \(\angle YLD\) are vertical angles. By the vertical angles theorem, vertical angles are congruent. So \(\angle RDL\cong\angle YLD\).

Step4: Analyze \(\angle GLH\cong\angle XGL\)

\(\angle GLH\) and \(\angle XGL\) are alternate - exterior angles. If \(SX\parallel HV\), then by the alternate - exterior angles theorem, \(\angle GLH\cong\angle XGL\).

Step5: Analyze \(\angle YLV\cong\angle DGL\)

\(\angle YLV\) and \(\angle DGL\) are not vertical angles, and there is no information (such as parallel lines and transversal relationships) to suggest they are congruent.

Answer:

\(\angle NLV\cong\angle DGN\), \(\angle RDL\cong\angle YLD\), \(\angle GLH\cong\angle XGL\)