x = 20°
BE doesnot bisect ∠EBC
Explanation:
a) m∠CBD = 55° , m∠DBE = 3x - 5 and m∠ABE = 4x - 10
m∠CBD + m∠DBE + m∠ABE = 180° (sum of angles on a line)
55° + 3x - 5 + 4x - 10 = 180
40 + 7x = 180
collect like terms:
7x = 180 - 40
7x = 140
x = 140/7
x = 20°
b) For a line to bisect an angle, it means it divided the angle into two equal parts.
To determine if BE bisect ∠EBC, we need to determine the two angles
∠DBE = 3x - 5 = 3(20) - 5 = 60 -5
∠DBE = 55
m∠ABE = 4x - 10 = 4(20) - 10 = 80 -10
m∠ABE = 70
From the diagram, EB doesn't divide ∠EBC. DB does.
BE is part of angle EBC
Hence, BE does not bisect ∠EBC