Question

select the correct answer from each drop - down menu
given: \\( \angle 1 \\) is complementary to \\( \angle 2 \\)
\\( m \angle 4 = 40 ^ { \circ } \\)
prove: \\( m \angle 2 = 50 ^ { \circ } \\)
complete the proof in paragraph form.
\\( \angle 1 \\) is complementary to \\( \angle 2 \\)
\\( m \angle 1 + m \angle 2 = 90 ^ { \circ } \\)
given
\\( \angle 4 \cong \angle 1 \\)
\\( m \angle 4 = m \angle 1 \\)
definition of complementary
definition of congruence
vertical angles theorem
\\( 40 ^ { \circ } = m \angle 1 \\)
substitution property of equality
\\( 4 = 40 ^ { \circ } \\)
given
by the substitution property of equality and the subtraction property of equality, since \\( \angle 1 \\) is complementary to \\( \angle 2 \\), \\( m \angle 1 + m \angle 2 = 90 ^ { \circ } \\). by the vertical angles theorem and the definition of congruence. combined with the given equation, \\( m \angle 4 = 40 ^ { \circ } \\), the substitution property of equality, \\( 40 ^ { \circ } + m \angle 2 = 90 \\) degrees, \\( m \angle 2 = 50 ^ { \circ } \\)

Explanation:

Step1: Substitute \(m\angle1\) with \(40^{\circ}\) in \(m\angle1 + m\angle2=90^{\circ}\)

Since \(m\angle1 = 40^{\circ}\) (from substitution property of equality as \(m\angle4=m\angle1\) and \(m\angle4 = 40^{\circ}\)), we have \(40^{\circ}+m\angle2 = 90^{\circ}\).

Step2: Solve for \(m\angle2\)

Using the subtraction property of equality (\(a + b=c\Rightarrow b=c - a\)), we get \(m\angle2=90^{\circ}-40^{\circ}\).

Answer:

First blank: subtraction property of equality; Second blank: \(90\) degrees.