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. Practice 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.