Question

Can someone help me with thisin the diagram shown it is know that A, B and C are collinear with m∠CBD = 55° , m∠DBE = 3x - 5 and m∠ABE = 4x - 10 (a) algebraically determine the value of x(b) does BE bisect ∠EBC Justify your response

Answer 1

x = 20°

BE doesnot bisect ∠EBC

Step-by-step 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