Question

Park 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. Select all that apply.

1) m∠def=92°
2) m∠deg=92°
3) m∠feh=88°
4) m∠deh=92°
5) m∠geh=88°

Answer 1

To identify the true statement, we need to analyze the angles formed by the intersecting pathways. The correct statements are m∠deg = 92°, m∠feh = 88°, and m∠deh = 92°.

Step-by-step explanation:

To identify the true statement, we need to analyze the angles in the given scenario. It is stated that m∠ged = 88°. Since the intersecting pathways form angles with the angle m∠ged, we can determine the true statements:

1. m∠def = 92° (Not correct because the angles formed by intersecting pathways are supplementary, so m∠def = 180° - m∠ged = 180° - 88° = 92°)
2. m∠deg = 92° (Correct because m∠deg is supplementary to m∠ged, so m∠deg = 180° - m∠ged = 180° - 88° = 92°)
3. m∠feh = 88° (Correct because m∠feh is the same as m∠ged since they are opposite angles formed by the intersecting pathways)
4. m∠deh = 92° (Correct because m∠deh is supplementary to m∠ged, so m∠deh = 180° - m∠ged = 180° - 88° = 92°)
5. m∠geh = 88° (Not correct because m∠geh is the same as m∠ged since they are opposite angles formed by the intersecting pathways)