Question

21 and 2 are vertical angles. If m21 = (6x + 21)° and m/2 = (5x+ 25)®, then find the value of x.

Answer 1

`$\text{If }\angle 21 \text{ and } \angle2 \text{ are vertical angles, then } \angle 2 \text { and }\angle 21 \text{ are congruent.}`
`\text{Since } \angle 2 \text { and } \angle 21 \text{ are congruent, their measures are equal.}`

`\text{So, we have:}`

`\text{m}\angle2 = \text{m}\angle21`

`6x + 21 = 5x + 25`

`x+21 = 25`

`x=4`.

So, the answer is x=4.

Answer 2

To find the value of x for the vertical angles, set the two expressions (6x + 21) and (5x + 25) equal to each other since vertical angles are congruent. After solving the equation, we determine that x equals 4.

Step-by-step explanation:

The question requires us to find the value of x given two expressions for the measures of vertical angles, which are equal. We have m21 = (6x + 21)° and m/2 = (5x+ 25)°. Since vertical angles are congruent, we can set these two expressions equal to each other and solve for x.

Setting the two expressions equal, we get:

1. 
   
3. (6x + 21) = (5x + 25)
4. 
   
6. 6x - 5x = 25 - 21
7. 
   
9. x = 4

The value of x that satisfies the equation is 4. Therefore, the measures of the angles can also be calculated by substituting x back into the expressions.