GRE question - What is greater z or 60? z is the degrees of a one of the congruent sidesAn isoceles triangle
To determine whether z is greater than 60 or not, we need to understand the properties of an isosceles triangle.
An isosceles triangle has two sides of equal length and two equal angles opposite those sides. In this case, z represents one of the congruent angles in the triangle.
Since an isosceles triangle has two equal angles and the sum of all three angles in any triangle is always 180 degrees, we can deduce the following:
Let x be the measure of each equal angle in the isosceles triangle.
Thus, the sum of the angles in the triangle can be expressed as:
x + x + z = 180
Since z is one of the congruent angles, we know that z = x.
Substituting z with x in the equation, we get:
2x + x = 180
3x = 180
x = 60
Therefore, each equal angle in the triangle measures 60 degrees. Since z is one of these equal angles, z is equal to 60 degrees as well.
So, z is not greater than 60; rather, z is equal to 60 degrees.