Question

1. a city planner is designing a park. he wants to place two pathways that intersect near the center of the park. if m∠ged = 88°, identify the true statement(s). a) m∠def = 92° b) m∠deg = 92° c) m∠feh = 88° d) m∠deh = 92° e) m∠geh = 88°

Explanation:

Step1: Recall vertical - angle and linear - pair properties

Vertical angles are equal and linear - pair angles are supplementary (sum to 180°). Given \(m\angle GED = 88^{\circ}\), \(\angle GED\) and \(\angle FEH\) are vertical angles, and \(\angle GED\) and \(\angle DEF\), \(\angle GED\) and \(\angle DEH\), \(\angle GED\) and \(\angle GEH\) form linear - pairs.

Step2: Calculate angle measures using properties

Since vertical angles are equal, \(m\angle FEH=m\angle GED = 88^{\circ}\). Also, for a linear - pair with \(\angle GED\) and \(\angle DEF\), \(m\angle DEF=180^{\circ}-m\angle GED = 180 - 88=92^{\circ}\), for \(\angle GED\) and \(\angle DEH\), \(m\angle DEH = 180^{\circ}-m\angle GED=92^{\circ}\), for \(\angle GED\) and \(\angle GEH\), \(m\angle GEH=180^{\circ}-m\angle GED = 92^{\circ}\).

Answer:

C. \(m\angle FEH = 88^{\circ}\)