Question

∠l and ∠m are complementary, ( 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
☐ ( 6x + 36 = 90 ) ☐ ( mangle l = mangle m )
☐ ( mangle l + mangle m = 90^circ ) ☐ ( mangle l + mangle m = 180^circ )
☐ ( 6x + 36 = 180 ) ☐ ( 2x + 25 = 4x + 11 )

Explanation:

1. Conceptual Set Up: Complementary angles sum to \(90^\circ\), so the correct relationship is \(m\angle L + m\angle M = 90^\circ\).
2. Algebraic Set Up: Substitute \(m\angle L = 2x + 25\) and \(m\angle M = 4x + 11\) into the complementary angle equation: \((2x + 25)+(4x + 11)=90\). Simplify the left - hand side: \(2x+4x + 25 + 11=6x+36\). So the algebraic set up is \(6x + 36=90\).

Answer:

Conceptual Set Up: \(m\angle L + m\angle M = 90^\circ\)
Algebraic Set Up: \(6x + 36 = 90\)