Find the measure of <4 in the figure

M<4= __? HELP PLS

82º

Step-by-step explanation:

Two of the lines are parallel and are indicated by the pink arrow. The other line is a transversal cutting through it, forming eight different angles. We are given the measure of one angle, and that is 82º.

Now alternate interior angles are equal to one another, and in this case, the angle with 82º and <8 are alternate interior angles. Likewise, the angle with 82º and <4 are also a pair of alternate interior angles. Therefore, <4 also equals 82º.

Another way we could do this is solve for <6. Since the angle with 82º and <6 are supplementary (form a total angle of 180º), we just have to subtract 82 from 180 to get 98. <6 = 98º.

Now, <6 and <7 are alternate interior angles, so both equal 98º, while <8 equals 82º (again, they're all alternate interior angles). So, if <8 is 82º, then its corresponding angle is <4. Corresponding angles are also equal to one another.