Question

Find the measures of the labeled angles.

((76 - x)∘ =)
(3x∘ =)

a. ((76 - x)∘ = 76, 3x∘ = 180)
b. ((76 - x)∘ = 76, 3x∘ = 76)
c. ((76 - x)∘ = 76 - x, 3x∘ = 76)
d. ((76 - x)∘ = 180, 3x∘ = 76)

Answer 1

The measures of the angles ((76 - x)∘ = 76, 3x∘ = 76). Thus, the correct answer is option b. ((76 - x)∘ = 76, 3x∘ = 76).

Step-by-step explanation:

In the given problem, the first equation is ((76 - x)∘ =) and the second equation is (3x∘ =). The correct answer is option b, which states that ((76 - x)∘ = 76, 3x∘ = 76).

Let's break down the solution for clarity:

1. For the first equation ((76 - x)∘ =), the angle is equal to 76 degrees.

(76 - x)∘ = 76

Solving for x:

76 - x = 76

x = 0

So, the value of x is 0.

2. For the second equation (3x∘ =), the angle is equal to 76 degrees.

3x∘ = 76

Solving for x:

3x = 76

`\[ x = (76)/(3) \]`

Thus, the solution for x is
`\((76)/(3)\).`

Putting it all together, the correct answer is ((76 - x)∘ = 76, 3x∘ = 76), and the value of x is
`\((76)/(3)\).` Option b accurately represents this solution. Therefore, the correct answer is option b. ((76 - x)∘ = 76, 3x∘ = 76).