The bisector splits this shape into two triangles. It is easier if we find the degrees of each triangle in this shape separately
We know that one angle of the top triangle is 65 degrees. Since another angle is congruent to the known angle we can assume that the other angle is 65 degrees as well. You can see this labeled in the image below.
The sum of all the angles of a triangle is 180 degrees. Since we know the degrees of two angles, which are both 65 degrees, we can make a formula to find the third angle:
180 = 65 + 65 + x
180 = 130 + x
50
This means that the last angle is 50 degrees
^^^We need to know this so that we can find the angle complimentary to the 50 degree angle, which will be the angle that is included in the bottom triangle
Complimentary angles are angles who's sum is 90 degrees. You can find the 50 degree angles complimentary angle by making a formula like so:
90 = 50 + x
40
Now we have the first angle of the second triangle. The second two angles can be found easily. Since the other two angles are congruent all we need to do is subtract 40 from 180 then divide the answer by 2 like so:
180 - 40 = 140
140 / 2 = 70
The other two angles are 70 degrees!
The measure of angle 2 is supplementary to one of the 70 degree angles. This means that you can find the value of angle 2 by subtracting 70 from 180
180 - 70 = 110
To find x set the equation equal to 110 and solve
110 = x + 120
x = -10
Hope this helped!
~Just a girl in love with Shawn Mendes