Question

If 1 = 2x + 6 and 2 = -x + 24, find 1 and 2.

Answer 1

Given:

∠1 = 2x+6 ans ∠2= -x+24

To find the values of ∠1 and ∠2.

Formula:

The values of the vertical angles are always equal.

Here,

∠1 and ∠2 are vertical angles.

So, by this condition,

∠1=∠2

or,
`2x+6 = -x+24`

or,
`2x+x = 24-6` [ Taking all the variables in one side and all the constant in other side]

or,
`3x = 18\\`

or,
`x = (18)/(3)`

or,
`x = 6`

So,

∠1 =
`2(6)+6 = 18^\circ`

∠2 =
`-6+24 = 18^\circ`

Hence,

The values of ∠1 and ∠2 are 18°.