Answer :
- 15. m∠ABE = 20°
- 16. m∠EBD = 22°
Given :
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°