SOLUTION: this problem is confusing me could someone please help?
In the triangle, ABC, Angle A is congruent to angle B and the measure of angle A is 54 degrees. Between line segment B an
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Question 103124: this problem is confusing me could someone please help?
In the triangle, ABC, Angle A is congruent to angle B and the measure of angle A is 54 degrees. Between line segment B and C The problem is 7x-6 and between line segment A and C The line segment is 5x.
It says to find the value of segment AC.
I need help badly.
Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
Ok from what I understand this is the triangle we are looking at:
Ok first we are told that:
In the triangle, ABC, Angle A is congruent to angle B and the measure of angle A is 54 degrees.
Congruent basically means that the angles equal one another.
so if angle A is 54 degrees then
angle B is also 54 degrees
Any time you have a triangle with two congruent angles we automatically know that the sides opposite those angles are congruent sides
Or in other words the triangle is an isosceles triangle.
Now if I understand your question correctly
line segment BC equals 7x-6
and
line segment AC equals 5x
So by definition of an isosceles triangle these two line segements are equal
so that gives us a simple equation to solve for x
7x - 6 = 5x
first add 6 to both sides
7x - 6 + 6 = 5x + 6
6's on the left side cancel out and we are left with
7x = 5x + 6
now subtract 5x from both sides
7x - 5x = 5x - 5x + 6
5x's on the right side cancel out and so
7x - 5x = 6
subtract 5x from 7x
2x = 6
finally solve for x by dividing both sides by 2
2x/2 = 6/2
x = 3
so the value of line segment AC is 15 because
5x
5*3 = 15
AND line segment BC is also 15 because
7x-6
7(3)-6
21-6 = 15
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