Answer:
1). Option B.
2). Option C.
3). Option A.
4). Option C.
5). Option D.
6). Option C.
Step-by-step explanation:
1). Bisector of angle ABC is,
Option (B). stack BD with rightwards arrow on top.
2). Since GH = GI [Given]
3x = 5x - 10
5x - 3x = 10
2x = 10
x = 5
Therefore, GH = 3x
= 3(5)
= 15
Option (C). is the answer.
3). Since m∠ABD ≅ m∠DCB [Given]
and m∠DCB ≅ m∠CBE [Since GH ≅ GI]
Therefore, m∠ABD ≅ m∠CBE
10y = 8y + 4
10y - 8y = 4
2y = 4
y = 2
Option (A). is the answer.
4). m∠DBE = m∠DBC + m∠CBE
= 10y + (8y + 4)
= (18y + 4)°
By putting y = 2,
m∠DBE = 18×2 + 4
= 36 + 4
= 40°
Option (C) will be the answer.
5). m∠ABE = m∠ABD + m∠DBC + m∠CBE
= 10y + 10y + (8y + 4)
= 28y + 4
= 28×2 + 4
= 56 + 4
= 60°
Option (D) will be the answer.
6). If m∠FBA = 7x + 6y
By putting x = 5 and y = 2
m∠FBA = 7(5) + 6(2)
= 35 + 12
= 47°
Option (C) will be the answer.
