SOLUTION: In isosceles ABC, B is the vertex. The measure of B can be represented as (8x-6). The measure of A can be represented as (3x+2). Find the measure of all three angles of the triangl
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Question 237386: In isosceles ABC, B is the vertex. The measure of B can be represented as (8x-6). The measure of A can be represented as (3x+2). Find the measure of all three angles of the triangle
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I presume that you mean B to be the angle that is different in measure from the other two angles in the isosceles triangle. The word vertex is used incorrectly in this context. All triangles, regardless of their configuration have three vertices. In an isosceles triangle, two of the vertices have angles that are equal in measure.
Given a correct assumption on my part, if B is the unequal angle, then angle A must be congruent to angle C, hence their measures are equal. Therefore if angle A measures 
then angle C must measure also.
We know that the sum of the measures of the interior angles of a triangle is 180 degrees or 
radians.
So we can say:
\ +\ (3x\ +\ 2)\ +\ (3x\ +\ 2)\ =\ 180\ \Rightarrow\ 14x\ -\ 2\ =\ 180\ \Rightarrow\ 14x\ -\ 2\ =\ 180\ \Rightarrow\ x\ =\ 13)
From which you can calculate:
\ -\ 6\ =\ 98)
degrees.
and
\ +\ 2\ =\ 41)
degrees.
Check:
or
\ +\ (3x\ +\ 2)\ +\ (3x\ +\ 2)\ =\ \pi)
From which you can calculate
radians
and
radians
Check:
John
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