Question

∠l and ∠m are supplementary, m∠l = 3x + 90 and m∠m = 2x − 20. select the correct geometric set up and the correct algebraic set up that you would use to determine the measure of each angle.

• ( 3x + 90 = 2x - 20 )
• ( mangle l + mangle m = 90^circ )
• ( mangle l + mangle m = 180^circ )
• ( mangle l = mangle m )
• ( 5x + 70 = 90 )
• ( 5x + 70 = 180 )

Explanation:

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\), so \(m\angle L + m\angle M = 180^\circ\).

Step2: Substitute angle expressions

Substitute \(m\angle L = 3x + 90\) and \(m\angle M = 2x - 20\) into the equation:
\((3x + 90) + (2x - 20) = 180\).
Simplify: \(5x + 70 = 180\).

Answer:

Geometric Set Up: \(m\angle L + m\angle M = 180^\circ\)
Algebraic Set Up: \(5x + 70 = 180\)