I can't figure out this problem, help would be much appreciated! Suppose line BC bisects angle ABE, and D is the interior of angle ABC. If m-angle CBD=28 degrees, and m-angle ABE=136 degrees, find m-ABD.
Since BC bisects ∢ABE , m∢ABC = 68°
so, m∢ABD = 68 - 28 = 40°
To find the measure of angle ABD, we can use the angle bisector theorem.
The angle bisector theorem states that in a triangle, if a line bisects an angle of the triangle, it divides the opposite side into segments that are proportional to the adjacent sides.
In this case, line BC bisects angle ABE, meaning that angle ABD and angle DBE are equal.
Let's assign the length of segment AB as 'x', and the length of segment BC as 'y'. Since BC bisects angle ABE, it divides segment AB into two equal parts, so the length of segment BD is also 'x'.
Now, we know that angle CBD is given as 28 degrees, and angle ABE is given as 136 degrees.
Since angle ABD and angle DBE are equal, let's represent their measure as 'm', so we have:
m + m + 28 + 136 = 180 (sum of angles in a triangle is 180 degrees)
2m + 164 = 180
2m = 180 - 164
2m = 16
m = 16/2
m = 8
So, the measure of angle ABD is 8 degrees.
To find the measure of angle ABD, we can use the fact that line BC bisects angle ABE.
First, we know that the measure of angle CBD is 28 degrees. Since line BC bisects angle ABE, this means that angle ABD is congruent to angle CBD. So, m-angle ABD = m-angle CBD = 28 degrees.
Therefore, the measure of angle ABD is 28 degrees.