Question

Help me on geometry??

Answer 1

15. ∠ABE = 50°

16. ∠EBD = 10n - 19

Explanation:

If
`$ \overline{\textbf{BE}} $` bisects ∠ABD then we have ∠ABE = ∠DBE

So, we will have: (6x + 2)° = (8x - 14)°

⇒ 6x + 2 = 8x - 14

⇒ 8x - 6x = 14 + 2

⇒ 2x =16

⇒ x = 8

∴ ∠ABE = 6(8) + 2

= 48 + 2

= 50°

∴∠ABE = 50°

16. If
`$ \overline{\textbf{BE}} $` bisects ∠ABD then ∠ABE + ∠EBD = ∠ABD

⇒(12n - 8) + ∠EBD = (22n - 11)

⇒ ∠EBD = 22n - 11 - 12n + 8

⇒ ∠EBD = 10n - 3

Hence, the answer.