Question

Given that ∠ABD = 71°, which equation could be used to solve problems involving the relationships between ∠DBC and ∠ABC?

A) (4a + 12) = (6a + 9)
B) 71 = (4a + 12) + (6a + 9)
C) (4a + 12) − (6a + 9) = 71
D) (4a + 12) + 71 = (6a + 9)

Answer 1

B) (9 + 12a) + (3a + 7) = 76

Explanation:

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Answer 2

Since the entirety of ∠ABD is 71 degrees, the sum of its two adjacent angles, angles DBC and ABC, will be equal to 71 degrees.

This means we'd use the following equation to solve for a.

71 = (4a + 12) + (6a + 9)

Answer:
B) 71 = (4a + 12) + (6a + 9)


To solve for a, combine like terms, subtract 21 from both sides, and divide both sides by 10.

71 = 4a + 12 + 6a + 9
71 = 10a + 21
50 = 10a
5 = a
a = 5