Question

Given that BE bisects ABD below, find each of the following

Answer 1

• 15. m∠ABE = 20°
• 16. m∠EBD = 22°

Given :

• BE bisects ∠ABD

To find :

• m∠ABE if m∠ABE = (6x + 2)° & m∠DBE = (8x - 14)°
• m∠EBD if m∠ABE = (12n - 8)° and m∠ABD = (22n - 11)°

Solution :

We know that the bisector divides the angle into two equal half

therefore,

• m∠ABE = m∠EBD....(1)
• m∠EBD + m∠ABE = m∠ABD....(2)

#15

• m∠ABE = (6x + 2)°
• m∠DBE = (8x - 4)°

From equation (1)

• m∠ABE = m∠DBE
• (6x + 2)° = (8x - 4)°
• 8x - 6 x = (4 + 2)°
• 2x = 6°
• x = 3°

Thus,

• m∠ABE = (6x + 2)° = (6*3 + 2)° = 20°

Hence, m∠ABE = 20°

#16

• m∠ABD = (22n - 11)°
• m∠ABE = (12n - 8)°

from equation (1)

• m∠ABE = m∠EBD = (12n - 8)°

from equation (2)

• m∠EBD + m∠ABE = m∠ABD
• (12n - 8)° + (12n - 8)° = (22n - 11)°
• 12 n + 12n - 8° - 8° = 22n - 11°
• 24n - 16° = 22n - 11°
• 24n - 22n = 16° - 11°
• 2n = 5°
• n = 5°/2
• n = 2.5°

Thus,

• m∠EBD = (12n - 8)° = (12*2.5°) - 8° = 22°

Hence, m∠ABD = 22°