Question

use the given information to prove that m∠2 = m∠3. given: m∠rst = m∠vut, m∠1 = m∠4. prove: m∠2 = m∠3. 1. m∠rst = m∠vut (given) 2. m∠1 = m∠4 (given) 3. blank (reason?)

Explanation:

Step1: Express angles in parts

We know that \(m\angle RST=m\angle1 + m\angle2\) and \(m\angle VUT=m\angle3 + m\angle4\).

Step2: Substitute using given equal - angles

Since \(m\angle RST = m\angle VUT\) (given) and \(m\angle1 = m\angle4\) (given), we substitute into the angle - sum equations: \(m\angle1 + m\angle2=m\angle3 + m\angle4\).

Step3: Use the substitution property

Substitute \(m\angle1\) for \(m\angle4\) in the equation \(m\angle1 + m\angle2=m\angle3 + m\angle4\). We get \(m\angle1 + m\angle2=m\angle3 + m\angle1\).

Step4: Subtract \(m\angle1\) from both sides

By the subtraction property of equality, \((m\angle1 + m\angle2)-m\angle1=(m\angle3 + m\angle1)-m\angle1\). This simplifies to \(m\angle2 = m\angle3\).

Answer:

\(m\angle2 = m\angle3\)