If the measure of angle 5 = (115) degrees and the measure of angle 8 = (6x + 1) degrees, what is the value of x?

Question

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Captionless Image
12
5
14
19

Answer 1

To find the value of $x$, we need to establish the relationship between angle 5 and angle 8. Based on the information given, if angle 5 and angle 8 are related, it's likely that they are complementary, supplementary, or form some other angle relationship based on their placement (like corresponding, alternate interior, etc.).

However, without the image, let's assume that angle 5 and angle 8 are supplementary angles, meaning their sum is $180$ degrees.

Given:

• Measure of angle 5 = ${115}^{\circ }$
• Measure of angle 8 = $6x+1^{\circ }$

We can set up the following equation:

$$115+(6x+1)=180$$

Now, simplify and solve for $x$:

1. Combine like terms: $$115+6x+1=180$$ $$6x+116=180$$

2. Subtract $116$ from both sides: $$6x=64$$

3. Divide by $6$: $$x=\frac{64}{6}=\frac{32}{3}\approx 10.67$$

This does not yield one of the answer choices provided (12, 5, 14, 19). If we assume that angle 5 and angle 8 are equal:

$$115=6x+1$$

1. Subtract $1$: $$114=6x$$

2. Divide by $6$: $$x=\frac{114}{6}=19$$

Thus, $x=19$ matches one of the answer choices provided.

So, if angles 5 and 8 are equal, the correct answer is:

$$\boxed{{\displaystyle 19}}$$