SOLUTION: Could you please help me with this question about restriction on x? Would greatly appreciate if you could please share the steps to solve it.
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Question 1186436: Could you please help me with this question about restriction on x? Would greatly appreciate if you could please share the steps to solve it.
Found 2 solutions by greenestamps, MathLover1:Answer by greenestamps(13209) (Show Source):
In the figure, let the triangle be ABC, with angle A 70 degrees and angle B 55 degrees; let CD be the segment from vertex C to base AB.
Imagine point D moving along base AB.
The farthest to the right point D can be is just to the left of vertex B; that means angle x has to be greater than 55 degrees.
The farthest to the left point D can be is just to the right of vertex A. Since the angle sum in triangle ACD is 180 degrees, x has to be less than 110 degrees. (70 plus x has to be less than 180 degrees.)
ANSWER: x is greater than 55 degrees and less than 110 degrees
You can put this solution on YOUR website! given:
first angle
second
then third angle is
so, triangle is because two of the legs are the same, and it is divided in two triangles (one with angles and , the other with and potion of other angle)
then, angle is an angle for smaller triangle (with and portion of otherangle)
by definition of exterior angle, +portion of otherangle
so, conclusion is:
