A Guide to the GRE/Triangles

Triangles

The angles of a triangle add up to 180º.

In this triangle, c is equal to 60 because the angles of a triangle add up to 180º.

The greater the angle in a triangle, the greater the corresponding side.

Angle f is greater than angle g but less than angle h, because the corresponding sides are larger and smaller, respectively.

The Four Types of Triangles

Practice

1.

If FG is equal to GH but less than FH, then the measure of angle FGH must at least be greater than how many degrees?

2.

If i is 8 degrees greater than k and 4 degrees greater than j, what is the measure of i?

3.

If LM and MN both have lengths of 10, and angle LMN has a measure of 80º, what are the measures of the other two angles of the triangle, MLN and LNM?

1. The angle measure must be greater than 60º.

The angles of a triangle add up to 180º. The greater the length of a side of a triangle, the greater its opposite angle.

If FH is greater than the other two sides, its angle measure must be greater. If all three angles were equal, they would equal 60º (180º divided by 3), but since this side is greater, its opposing angle must be greater than 60º, while the other two must be less than 60º.

2. 64º

The angles of a triangle add up to 180º. Thus, i + j + k = 180.

i + j + k = 180. Take the initial equation.

i + (i - 4) + (i - 8) = 180 Substitute the known values of the other two variables in terms of i.

i + i -4 + i - 8 = 180 Expand the parentheses.

3i - 12 = 180 Consolidate the constants and variables.

3i = 192 Add 12 to both sides.

i = 64 Divide both sides by 3. i is equal to 64.

3. 50º

Since LM and MN have identical lengths, the angles opposite these sides have identical lengths. The angles of a triangle add up to 180º; thus, since the third angle is equal to 80º, the other two angles must have a combined measure of 100º. Since they are equal, the measure of each is 50º.