In a Rhombus, all four sides are congruent. Therefore, sides KH and KJ are congruent to each other.
These congruent sides form an Isosceles Triangle. By the Isosceles Triangle Theorem, if a triangle has a pair of congruent sides leading to the vertex, the base angles opposite of those sides are also congruent angles.
With this, let’s form an Algebraic equation since we don’t know the measure of angle HJK. We can use the Triangle Sum Theorem, which states all three interior angles in a triangle sum up to 180.° Let x=base angle measure.
126+x+x=180
Since x=base angle and there are two base angles, there must be two x in our equation. Keeping them the same variable denoted they are the same measure.
Solve for x:
Combine like terms:
126+2x=180
Subtract 126 from both sides:
2x=180-126
2x=54
Divide both sides by 2:
x=54/2
x=27
So, because angle HJK is a base angle, it measures 27.°