Question

I can't find the value of x or DEG, I've been stuck for a while.​

Answer 1

• x = 4
• ∠DEG = 32°

Explanation:

We know that:

• If a rectangle is divided by its diagonals, it will form 4 isosceles triangles (ΔDGH, ΔFHE, ΔGHF, ΔDHE).
• ΔFHE = 180 = 64 + 2y
• ΔGHF = Isosceles triangle [∠G = ∠F]

________________________________________________

• 180 = 64 + 2(FEH)
• => 116 = 2(FEH)
• => ∠FEH = 116/2 = 58

________________________________________________

• => 90 - 58 = ∠DEG
• => ∠DEG = 32°

________________________________________________

• => 90° = 6x + 8 + 58
• => 90° = 6x + 66
• => 90 - 66 = 6x
• => 24 = 6x
• => x = 4

________________________________________________