What is the measure of angle 3, in degrees, in the figure shown?

38 degrees.

Step-by-step explanation:

There are 180 degrees in a triangle, so

m<1 = 180 - (43 + 74)

=  180 - 117

= 63 degrees.

m < 2 = m < 1   ( opposite angles) so

m < 2 = 63 degrees.

Finally, m < 3 = 180 - (63 + 79)

== 180 -  142

= 38 degrees.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c