In isosceles triangle RST, the measure of angle R is 110 degrees. The lengths of sides RS and RT are equal. What is the…

The sum of the angle measures in a triangle is 180 degrees. The problem states that in isosceles triangle RST, the lengths of sides RS and RT are equal. In an isosceles triangle, the angles opposite the equal sides are also equal.

Therefore, the measure of angle S is equal to the measure of angle T. Let x be the measure of angle S. Then the measure of angle T is also x. The sum of the angles in the triangle can be written as 110 + x + x = 180. Combining terms gives 110 + 2x = 180. Subtracting 110 from both sides gives 2x = 70. Finally, dividing by 2 gives x = 35. The measure of angle S is 35 degrees.

Choice A is incorrect; this may result from incorrectly dividing the given angle by 2.

Choice C is incorrect; this is the sum of angles S and T, not the measure of angle S alone.

Choice D is incorrect; if angle S were 110 degrees, the sum of just two angles (R and S) would be 220 degrees, which already exceeds the 180-degree sum for a triangle.