Question

What is m angle A B E?

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

What is m angle D B E?

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

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

What is the value of y?

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

Answer 1

• ∠ABE = 60°
• ∠DBE = 40°
• ∠FBA = 47°
• y = 2

Explanation:

The various markings tell you that ...

GH = GI

5x -10 = 3x

2x = 10

x = 5

and

∠ABD ≅ ∠DBC

10y° = (8y+4)°

2y = 4

y = 2

The markings on GH and GI tell you that ΔGBI ≅ ΔGBH, so ...

∠CBE ≅ ∠DBC ≅ ∠ABD = 10y° = 20°

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A) m∠ABE = 60° . . . matches choice D

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B) m∠DBE = 40° . . . matches choice C

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C) m∠FBA = 7(5) +6(2) = 35 +12 = 47 . . . matches choice C

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D) The value of y is 2. . . . matches choice A