Question

Which ray is a bisector of angle A B C?

Select one:
A. stack B C with rightwards arrow on top
B. stack B D with rightwards arrow on top
C. stack B A with rightwards arrow on top
D. stack B F with rightwards arrow on top

What is GH?

Select one:
A. 5
B. 10
C. 15
D. 25

What is the value of y?

Select one:
A. 2
B. 4
C. 16
D. 20

What is m angle D B E?

Select one:
A. 20
B. 30
C. 40
D. 50

What is m angle A B E?

Select one:
A. 20
B. 30
C. 40
D. 60

If m angle F B A equals 7 x plus 6 y, what is m angle F B A?

Select one:
A. 40
B. 44
C. 47
D. 60

Answer 1

1). Option B.

2). Option C.

3). Option A.

4). Option C.

5). Option D.

6). Option C.

Explanation:

Answer 2

1). Option B.

2). Option C.

3). Option A.

4). Option C.

5). Option D.

6). Option C.

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.