ANSWER:
x = 11
OR
x = - 5
In triangle ABC displayed in the diagram, the value of ( x ) is 11 or - 5.
Explanation:
In triangle ABC, AB is equivalent to AC. This means that the triangle is an isosceles triangle as two sides are equivalent in length.
Since triangle ABC is an isoceles triangle, the base angles must be equivalent to each other.
( x^2 - 6x )° and 55° are both base angles of the isosceles triangle ABC.
THEREFORE:
x^2 - 6x = 55
x^2 - 6x - 55 = 0
x^2 - 11x + 5x - 55 = 0
x ( x - 11 ) + 5 ( x - 11 ) = 0
( x - 11 ) ( x + 5 ) = 0
Solution No. 1 -
x - 11 = 0
x = 11
Solution No. 2 -
x + 5 = 0
x = - 5