Answer x=125
We are given an isosceles triangle because two sides are marked congruent, and therefore, the base angles opposite those sides are congruent. First we need to calculate the angles of the triangle using the Isosceles Triangle Theorem.
We are given a 110° angle with a ray that forms a straight line. Straight lines measure 180° by definition. So, we can calculate the vertex angle in the triangle by creating this equation:
110+x=180
110 degrees plus x creates a 180 degree line. Now, solve for x:
x=70
We have our first angle in the triangle, and we know a triangle must sum up to 180°. We also know the triangle is isosceles, and so the two base angles are congruent. We can create another equation to find all angles in the triangle:
70+2x=180
Remember, we have one angle and because the two base angles are congruent, we can denote them with the same variable and multiply by 2 because the angles will add to each other twice. Solve for x:
2x=110
x=55
So, we now have all there angles and can solve for “x.” Like we did before, a straight line forms one of the rays of the angle. So, we can create the equation:
55+x=180
55° plus x° sums up to 180. Now, solve for “x:”
x=125