A Guide to the GRE/Lines and Angles
Lines & Angles
Opposite angles are equal. Adjacent angles on a line add up to 180º.
- Angles n and p are equal.
- Angles q and o are equal.
- Angles n and o add up to 180º.
- Angles o and p add up to 180º.
- Angles p and q add up to 180º.
- Angles q and n add up to 180º.
A line intersecting two parallel lines forms the same angles with each.
Parallel lines are those which are a constant distance apart. A line intersecting them is known as a “transversal.”
Assume both sets of lines are parallel; therefore:
- Angles f and g are equal.
- Angles h and i add up to 180º.
- Angles f and h are equal.
- Angles g and i add up to 180º.
1. In this figure, both pairs of lines are parallel, and w is 10º greater than u. What are the measures of angles t, u, v and w?
Answers to Practice Questions
1. t, u, v, and w have measures of 95º, 95º, 85º, and 95º, respectively.
Because lines make the same angles through any parallel lines they intersect, angle w is identical to angle v as well as the angle directly opposite t. Because opposite angles are equal, angles t and w are equal.
All three of these angles are equal to either of the angles adjacent to angle u along the line (either the line running from t to u or from v to u); thus u + v = 180º. Since w = u + 10º, we can solve for u.
u + v = 180º Take the initial equation.
u + (u + 10º) = 180º Substitute for v in terms of u.
2u + 10º = 180º Add the variables.
2u = 170º Subtract 10º from both sides.
u = 85º Divide both sides by 2. u is 85º, making the other three angles 95º.