Question

∠l and ∠m are supplementary, ( mangle l = 2x + 25 ) and ( mangle m = 4x + 11 ). select the correct geometric set up and the correct algebraic set up that you would use to determine the measure of each angle.
□ ( 2x + 25 = 4x + 11 )
□ ( 6x + 36 = 90 )
□ ( 6x + 36 = 180 )
□ ( mangle l = mangle m )
□ ( mangle l + mangle m = 180^circ )
□ ( mangle l + mangle m = 90^circ )

Explanation:

Step1: Recall Supplementary Angles Definition

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

Step2: Substitute Angle Expressions

Substitute \(m\angle L = 2x + 25\) and \(m\angle M = 4x + 11\) into the geometric setup:
\((2x + 25) + (4x + 11) = 180\).

Step3: Simplify the Equation

Combine like terms: \(2x + 4x + 25 + 11 = 180\) → \(6x + 36 = 180\).

Answer:

Geometric Set Up: \(m\angle L + m\angle M = 180^\circ\)
Algebraic Set Up: \(6x + 36 = 180\)