Determine if the two triangles are Isosceles:
Because triangles ABC and JKL are similar, sides BC and KL must be proportional. We see that triangle JKL has two congruent sides lengths opposite of the base angles, making triangle JKL Isosceles. Therefore, triangle ABC must also have two corresponding, proportional side lengths that are also congruent to each other and opposite the base angles, making triangle ABC Isosceles, too. So, side BC must also be 5, since the two sides opposite of the base angles must be congruent in an Isosceles Triangle.
Properties of Isosceles Triangles:
When the two sides opposite of the base angles are congruent in a triangle, the triangle is Isosceles, and those base angles must also be congruent.
Solving for angle measures:
We can now apply the Triangle Sum Theorem: all three interior angles in a triangle must sum up to 180.° This will allow us to solve for the measure of angle B.Let’s create an equation:
48+x+x=180
The variable “x” is used to denote an unknown angle value. Notice that there are two “x” in the equation. This is because we know these two base angles will be congruent, thus they can use the same variable.
Simplify:
48+2x=180
Solve for x:
Subtract 48 from both sides:
2x=180-48
2x=132
Divide both sides by 2:
x=132/2
x=66
Therefore, the two base angles measure 66.° One of these base angles is angle B, and because the base angles are congruent, m∠B=66.°