If bd is perpendicular to ac m angle dbe equals 2x - 1 + m angle cbe equals 5x - 42 find the value of x

I've drawn a graph in order to a better understanding of this problem. We know that:

BC is perpendicular to AC

∠DBE = 2x - 1

∠CBE = 5x - 42

Let's call the intersection of line BC and AC the point P, so:

∠P=90°

And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:

∠PCB = ∠CBE = 5x - 42

Moreover:

∠PBC = 2x - 1 - (5x - 42)

∠PBC = 2x - 1 - 5x + 42

∠PBC = -3x + 41

The internal angles of any triangle add up to 180°. Hence for ΔBPC:

90° + ∠PBC + ∠PCB  = 180°

90° - 3x + 41  + 5x - 42  = 180°

2x + 89 = 180

2x = 91

x = 45.5°

step-by-step explanation:

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