Find Angle Measures in a Square Using Diagonal and Interior Angle Properties

Question

In square DEFG with diagonals intersecting at H, find the measures of ∠EFG, ∠GDH, ∠FEG, and ∠DHG.

Accepted Answer

m∠EFG = 90°, m∠GDH = 45°, m∠FEG = 45°, m∠DHG = 90°

Answer

Step 1: All interior angles of a square are right angles, so ∠EFG = 90°. Step 2: The diagonals of a square bisect the interior angles. ∠GDH is half of the right angle ∠GDE, so $m∠GDH = \frac{90°}{2} = 45°$. Step 3: ∠FEG is half of the right angle ∠DEF, so $m∠FEG = \frac{90°}{2} = 45°$. Step 4: The diagonals of a square are perpendicular to each other, so the angle formed at their intersection ∠DHG = 90°.