Question

1. arrange the statements and reasons below in a logical order to complete the proof. given: \\( \angle 1 \\) and \\( \angle 2 \\) are complementary; \\( m \angle 1=28^{\circ} \\). prove: \\( m \angle 2=62^{\circ} \\) \\( 28^{\circ}+m \angle 2=90^{\circ} \\) substitution property \\( m \angle 1+m \angle 2=90^{\circ} \\) definition of complementary angles \\( m \angle 1=28^{\circ} \\) given \\( m \angle 2=62^{\circ} \\) subtraction property of equality \\( \angle 1 \\) and \\( \angle 2 \\) are complementary. given

Explanation:

Step1: Identify given statements

First, we have the given information: \(\angle1\) and \(\angle2\) are complementary (Given) and \(m\angle1 = 28^{\circ}\) (Given).

Step2: Use definition of complementary angles

By the definition of complementary angles, if two angles are complementary, the sum of their measures is \(90^{\circ}\). So \(m\angle1 + m\angle2=90^{\circ}\) (Definition of complementary angles).

Step3: Substitute the given measure

We know \(m\angle1 = 28^{\circ}\), so substitute this into the equation from step 2: \(28^{\circ}+m\angle2 = 90^{\circ}\) (Substitution Property).

Step4: Solve for \(m\angle2\)

Using the Subtraction Property of Equality, subtract \(28^{\circ}\) from both sides: \(m\angle2=90^{\circ}- 28^{\circ}=62^{\circ}\) (Subtraction Property of Equality).

Answer:

1. \(\angle1\) and \(\angle2\) are complementary. (Given)
2. \(m\angle1 = 28^{\circ}\) (Given)
3. \(m\angle1 + m\angle2 = 90^{\circ}\) (Definition of complementary angles)
4. \(28^{\circ}+m\angle2 = 90^{\circ}\) (Substitution Property)
5. \(m\angle2 = 62^{\circ}\) (Subtraction Property of Equality)