<PRE><B>Question 1125636</B>
the picture is, unfortunately, not accurate, which is enough to throw you off completely.


the geometric rule is that the exterior angle of a triangle is equal to the sum of the remote interior angles.


assuming that ABC = 86.33 degrees and BAC = 36.46 degrees, then angle BCD should have been 122.79 degrees.


i redrew the diagram to make angle BCD = 122.79 degrees rather than 122.6 degrees.


i also added point E because that was necessary for descriptive purposes.


my picture is shown below:


&lt;img src = &quot;http://theo.x10hosting.com/2018/100901.jpg&quot; alt=&quot;$$$&quot; &gt;


since the sum of the angles of a triangle is always 180 degrees, then angle BCA must be equal to 180 - 86.33 - 36.46 = 57.21 degrees.


there are other implications in the diagram that you were apparently not given.


one of them is that ABEC is a parallelogram.


as such, the opposite angles of the parallelogram have to be equal.


that makes angle BAC equal to angle BEC.


since ABEC is a parallelogram, then BE is parallel to AC and parallel to AD because AC and AD are segments of the same line.


since alternate interior angles of parallel lines are equal, that mekes angle ECD equal to angle BEC.


angle BCD is composed of angles BCE and ECD.


this means that angle BCE is equal to angle BCD minus angle ECD.


this means that angle BCE is equal to 122.79 minus 36.46 which make it equal to 86.33 degrees.


this may be enough to answer your questions.


those questions are:


Q1. How are the measures of the remote interior angles related to the measure of the exterior angle? Use the calculator to create an expression that confirms your conjecture. 


after correcting the diagram, the answer is that the sum of the remote interior angles of the triangle are equal to the exterior angle.


86.33 + 36.46 = 122.79.


Q2. Explain how the two angles that fill the exterior angle are related to the remote interior angles in the triangle. Explain how this demonstrates your conjecture from Q1.


the two angles that fill the exterior angle are angle BCE and angle ECD.


angle BCE is equal to angle ABC (alternate interior angles of parallel lines).


angle ECD is equal to angle BAC (corresponding angles of parallel lines).


boy, they really threw you a curve with this diagram.
unless i&#39;m missing something like the words that may have went with this picture, you weren&#39;t given nearly enough information to come up to these conclusions, and the information you were given in the diagram was simply wrong.


not also that angle CBE is equal to angle BCA (alternate interior angles of parallel lines).


this makes the corresponding angles of triangle ABC and triangle ECB congruent because all their corresponding angles are equal and their corresponding sides are congruent (opposite sides of a parallelogram are both parallel and equal).


lots of missing information made answering this difficult.
my assumptions are based on what i know of geometry that i applied to this diagram to make it fit what i know.


hopefully this helps.


note that there are further implications in the diagram that i didn&#39;t discuss.


those are:


triangle ABC is also congruent to triangle CED.


BEDC is also a parallelogram.


ABED is an isosceles trapezoid.


i&#39;m assuming these are also true but i didn&#39;t get into them because they are based on my assumptions on what is in the diagram that did not appear to be explained fully enough.







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