Question 1093325: Help! I have a problem, can anyone help me????
The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. find the measure of angle ABC if measurement of angle CBD = 16 degrees and measurement of angle ACB = 118.
I don't know where to go after the picture!!!!
Found 2 solutions by KMST, MathTherapy:
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! There is another point I want to name.
The perpendicular bisector of AB intersects AB at point M,
the midpoint of AB.
Below you see points A, B, C, D, and M labeled.
I drew triangle ABC, the perpendicular bisector of AB,
the extension of AC all the way to D.
I also drew segment BD, labeled the known angle measures,
and labeled the angle measure for angle ABC as  .
With that extra segment BD, we have two right triangles: AMD and BMD.
Both triangles (AMD and BMD) are right triangles, because they have a right angle at M.
Right triangle legs AM and MB are congruent, because M is the midpoint of AB.
The other leg of both triangles is MD.
Because they are right triangles with congruent pairs of legs,
triangles AMD and BMD are congruent.
Because Corresponding Parts of Congruent Triangles are Congruent,
angles BAD and ABD are congruent.
The measure (in degrees) of angle CBD is  .
The measure (in degrees) of angle CBD is .
The measure (in degrees) of angle ABD=ABC+CBD is  .
That is also the measure (in degrees) of BAD=BAC,
because BAD and ABD are congruent angles.
The sum of the measures of the angles of ABC is
 , so substituting
So, the measure of angle ABC is  .
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Help! I have a problem, can anyone help me????
The perpendicular bisector of side AB of triangle ABC intersects the extension of side AC at D. find the measure of angle ABC if measurement of angle CBD = 16 degrees and measurement of angle ACB = 118.
I don't know where to go after the picture!!!!
∡ABC = 
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