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, $x = \frac{18}{3}$

or, $x = 6$

So,

∠1 = $2(6)+6 = 18^\circ$

∠2 =$-6+24 = 18^\circ$

Hence,

The values of ∠1 and ∠2 are 18°.