We want to find the value of the variable x. To do so, we will start by identifying the type of triangle. Let's recall the classification of triangles.
A right triangle is a specific type of triangle that contains one angle of 90^(∘).
Since the given triangle has two congruent sides, triangle EHG is an isosceles triangle. Then, to find x, we will first consider Isosceles Triangle Theorem.
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Now, we can find x by using the Triangle Angle-Sum Theorem. Recall that this theorem states that the measures of the interior angles of a triangle add up to 180^(∘).
