Respuesta :
If two lines intersect in a point, then
Two pairs of opposite angles are formed
In your figure angle (x + 11) and angle (5x - 41) are opposite angles
the opposite angles are equal in measure, so
5x - 41 = x + 11
To solve this equation we need to put the variable in a side and the number on the other side, so
Subtract x from both sides to move x from the right side to the left side
[tex]5x-x-41=x-x+11[/tex]Add the like terms
[tex]4x-41=11[/tex]Now add both sides by 41 to move 41 from the left side to the right side
[tex]\begin{gathered} 4x-41+41=11+41 \\ 4x=52 \end{gathered}[/tex]Divide both sides by 4 to find x
[tex]\begin{gathered} \frac{4x}{4}=\frac{52}{4} \\ x=13 \end{gathered}[/tex]The value of x is 13
Now let us find the measure of each angle by substituting x by 13 in each angle
x + 11 = 13 + 11 = 24 degrees
5x - 41 = 5(13) - 41 = 65 - 41 = 24 degrees
The measure of each opposite angle = 24 degrees
