Question

∠l and ∠m are complementary, m∠l = 5x - 4 and m∠m = 3x - 6. select the correct geometric set up and the correct algebraic set up that you would use to determine the measure of each angle. options: m∠l + m∠m = 90°; m∠l = m∠m; m∠l + m∠m = 180° (left column); 5x - 4 = 3x - 6; 8x - 10 = 90; 8x - 10 = 180 (right column).

Explanation:

Step1: Recall Complementary Angles

Complementary angles sum to \(90^\circ\). So, \(m\angle L + m\angle M = 90^\circ\) is the correct geometric setup.

Step2: Substitute Angle Expressions

Substitute \(m\angle L = 5x - 4\) and \(m\angle M = 3x - 6\) into the geometric setup:
\((5x - 4)+(3x - 6)=90\)
Simplify the left - hand side: \(5x+3x-4 - 6=90\), which is \(8x - 10 = 90\). This is the correct algebraic setup.

Answer:

Geometric Set Up: \(m\angle L + m\angle M = 90^\circ\)
Algebraic Set Up: \(8x - 10 = 90\)