Question

suppose that two complementary angles are congruent. given: ∠1 and ∠2 are complementary, m∠1 = m∠2, m∠1 = 45 and m∠2 = 45. prove: m∠1 + m∠2 = 90. statements: 1. given 2. given 3. m∠1 + m∠2 = 90 4. substitution property 5. simplify 6. division property reasons: 1. given 2. given 3. 4. substitution property 5. simplify 6. division property

Explanation:

Step1: State given information

Given \(m\angle1 = m\angle2\) and \(m\angle1 + m\angle2=90^{\circ}\)

Step2: Substitute equal - angle values

Since \(m\angle1 = m\angle2\), we can substitute \(m\angle2\) with \(m\angle1\) in the equation \(m\angle1 + m\angle2 = 90^{\circ}\). So we get \(m\angle1+m\angle1 = 90^{\circ}\), which simplifies to \(2m\angle1=90^{\circ}\)

Step3: Solve for \(m\angle1\)

Using the division property, divide both sides of the equation \(2m\angle1 = 90^{\circ}\) by 2. We have \(m\angle1=\frac{90^{\circ}}{2}=45^{\circ}\)

Step4: Find \(m\angle2\)

Since \(m\angle1 = m\angle2\), then \(m\angle2 = 45^{\circ}\)

Answer:

The measure of each angle (\(\angle1\) and \(\angle2\)) is \(45^{\circ}\)