Question-189054

Question Number 189054 by mathlove last updated on 11/Mar/23

Answered by som(math1967) last updated on 11/Mar/23

∠ E B D = ∠ H B C, ∠ A B C = ∠ E B F

∠ H B F = ∠ A B D

∠ E B D + ∠ E B F + ∠ H B F + ∠ H B C

+ ∠ A B C + ∠ A B D = 360

2 (∠ E B D + ∠ H B F + ∠ A B C) = 360

∠ E B D + ∠ H B F + ∠ A B C = 180

∠ E B D + 40 + n + ∠ H B F + k + 55

+ ∠ A B C + m + 90 = 3 \times 180

m + n + k + 185 = 540 - 180

m + n + k = 360 - 185 = 175