Question

∠A and \angle B∠B are vertical angles. If m\angle A=(2x+1)^{\circ}∠A=(2x+1)

∘
and m\angle B=(8x-17)^{\circ}∠B=(8x−17)
∘
, then find the value of x.

Answer 1

To solve for x when given that ∠A and ∠B are vertical angles with measures (2x+1)° and (8x-17)° respectively, we set the measures equal to each other and solve the equation 2x + 1 = 8x - 17. After simplifying, we find that x = 3.

Step-by-step explanation:

Since ∠A and ∠B are vertical angles, they are congruent, meaning they have equal measures. Therefore, we can set their measures equal to each other to solve for x:

m∠A = m∠B

(2x+1)° = (8x-17)°

To find the value of x, we set up the following equation:

2x + 1 = 8x - 17

Now, we solve for x:

1. Subtract 2x from both sides:
2. 1 = 6x - 17
3. Add 17 to both sides:
4. 18 = 6x
5. Divide both sides by 6:
6. x = 3

The value of x is therefore 3.

Answer 2

2x + 1 = 8x -17

Add 17 to both sides:

2x + 18 = 8x

Subtract 2x from both sides:

18 = 6x

Divide both sides by 6:

x = 18/6

x = 3

Step-by-step explanation: