SAT Lines, angles, and triangles Question

Focused practice00:00

Question 1 · Hard · MathOctober 2024 Batch 2 · Q21Lines, angles, and triangles · 0 solved

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of these eight angles is $(7 x - 250)^{\circ}$ . The sum of the measures of four of the eight angles is $k^{\circ}$ . Which of the following could NOT be equivalent to $k$ , for all values of $x$ ?

Wrong answers are logged automatically — sign in after three questions to keep your mistake log and get memory-curve retests.

Read before you answer

Strategy

With a transversal across two parallel lines, there are only two distinct angle measures: an acute angle a and its supplement 180 − a. Any sum of four angles is determined by how many acutes and obtuses you include. Write the sum as t· $a + (4 - t) (180 - a)$ , list the resulting forms, then substitute a using the given angle or its supplement and see which expressions can (or cannot) arise.

Hints (open one at a time)

Hint 1

Across two parallel lines cut by a transversal, all acute angles are equal and all obtuse angles are equal, and they are supplements.

Hint 2

Express the sum of four angles by counting how many acute (t) and how many obtuse (4 − t) you pick, and simplify in terms of a.

Hint 3

Plug a in as either 7x − 250 or 430 − 7x and see which algebraic forms for the sum appear; one listed expression never shows up.

Step-by-step Explanation

Check your answer (or reveal it) to unlock the full walkthrough.