Question

move the yellow dots in order to make the segments intersect. let the intersection be called point n. make the lines intersect in such a way that ∠jnl is an obtuse angle greater than 135°. afterwards, use the protractor to determine the precise measure of all four angles. you should redraw the lines if ∠jnl is not the proper size. move the line segments to intersect at n ∠jnl should be an obtuse angle greater than 135° done moving lines

Explanation:

Step1: Move the yellow dots (K, J on one segment; M, L on the other) so that the two line segments intersect at point N. Arrange the segments such that the angle ∠JNL (formed at N by points J, N, L) is obtuse (greater than 90°) and specifically greater than 135°. Visually, this means the opening between JN and LN should be wide, more than a 135° angle (e.g., closer to 180° but still obtuse).

Step2: Once the lines intersect at N with ∠JNL > 135°, use a protractor to measure ∠JNL. Then, recall that vertical angles are equal, and adjacent angles are supplementary (sum to 180°). So if ∠JNL = x (x > 135°), then its vertical angle (opposite angle) is also x. The adjacent angles to ∠JNL will be 180° - x (each), and their vertical angles will also be 180° - x. For example, if ∠JNL is 150°, then the vertical angle is 150°, and the other two angles are 30° each (since 180 - 150 = 30).

Answer:

To solve:

1. Move the yellow - dot - marked segments (KJ and ML) to intersect at N, ensuring ∠JNL > 135° (obtuse).
2. Measure ∠JNL with a protractor. Let’s say ∠JNL = 150° (example, actual depends on drawing). Then:

• Vertical angle to ∠JNL (e.g., ∠KNM) = 150° (vertical angles are equal).
• Adjacent angles (e.g., ∠JNM and ∠LNK) = 180°−150° = 30° each (supplementary angles sum to 180°), and their vertical angles are also 30°.

(Note: The precise measure depends on the final position of the lines after moving the dots and using the protractor.)