Question

21 and 22 form vertical angles. L1=(18-91°, 22=(4x+3)°.

Answer 1

Vertical angles are opposite to each other when two lines cross, they share the same vertex. These angles are also called congruent, and they are always equal, which means that:

m∠1=m∠2

m∠1=(16x-9)º

m∠2= (4x+3)º

Using the expressions for both angles you can determine an equation and clear the value of x from it:

m∠1=m∠2

16x-9=4x+3

`\begin{gathered} 16x-9=4x+3 \\ 16x-4x=3+9 \\ 12x=12 \\ x=1 \end{gathered}`

Now that you know the value of x, you can replace it in either formula to determine the value of the angles:

m∠1=(16x-9)º= 16*1-9=7º

This means that m∠1=m∠2=7º