The angle EDG in the square is 40°, as determined by properties of bisected angles, perpendicular diagonals, and the sum of triangle angles.
To find the angle EDG, we need to use some properties of a square and its diagonals. Here are the steps:
First, we know that the diagonal EG bisects the angle DEG, so we can write ∠DEG = 2∠EDG.
Second, we know that the diagonal BD is perpendicular to the diagonal EG, so we can write ∠BDE = 90°.
Third, we know that the angle CDB is given as 50°, so we can write ∠CDB = 50°.
Fourth, we can use the fact that the sum of the angles in a triangle is 180° to write ∠BDE + ∠CDB + ∠EDB = 180°.
Fifth, we can substitute the values of ∠BDE and ∠CDB from the previous steps and solve for ∠EDB. We get ∠EDB = 180° - 90° - 50° = 40°.
Sixth, we can use the fact that the opposite angles of a square are equal to write ∠EDG = ∠EDB = 40°.
Therefore, the answer is ∠EDG = 40°.
The question probable may be:
If m∠CDB = 50°, what is m∠EDG?