Question

select the correct answer from each drop - down menu.
given: ∠1 is complementary to ∠2
m∠4 = 40°
prove: m∠2 = 50°
complete the proof in paragraph form.
∠1 is complementary to ∠2
m∠1 + m∠2 = 90°
given
definition of complementary
∠4 ≅ ∠1
m∠4 = m∠1
vertical angles theorem
definition of congruence
40° = m∠1
complete the proof in paragraph form
by the definition of complementary an ∠2. m∠1 + m∠2 = 90°. by the vertical angles theorem. ∠4 ≅ ∠1 and m∠4 = m∠1 by the definition d given equation. m∠4 = 40°, the substitution property of equality means that 40° = m∠1. using the 40° + m∠2 =
finally, using the m∠2 = 50°

Explanation:

Step1: Substitute \(m\angle1\) into the complementary - angle equation

We know that \(m\angle1 + m\angle2=90^{\circ}\) (definition of complementary angles) and \(m\angle1 = 40^{\circ}\) (since \(m\angle4 = m\angle1\) by the vertical - angles theorem and \(m\angle4 = 40^{\circ}\)). Using the substitution property of equality, we substitute \(m\angle1\) in the equation \(m\angle1 + m\angle2=90^{\circ}\). So, \(40^{\circ}+m\angle2 = 90^{\circ}\).

Step2: Solve for \(m\angle2\)

Using the subtraction property of equality, if \(40^{\circ}+m\angle2 = 90^{\circ}\), then \(m\angle2=90^{\circ}-40^{\circ}\).

Answer:

The first blank is filled with "substitution property of equality" and the second blank is filled with \(90^{\circ}\)