Question

I need help finding the variable and measure the angle.

Answer 1

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

`5x-x-41=x-x+11`

Add the like terms

`4x-41=11`

Now add both sides by 41 to move 41 from the left side to the right side

`\begin{gathered} 4x-41+41=11+41 \\ 4x=52 \end{gathered}`

Divide both sides by 4 to find x

`\begin{gathered} (4x)/(4)=(52)/(4) \\ x=13 \end{gathered}`

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