Question

complete the following proof
given: \\( \triangle s r q \\)
prove: \\( m \angle 1 + m \angle 2 + m \angle 3 = 180 ^ { \circ } \\)

Explanation:

Step1: Use the definition of a straight line

$$m\angle4 + m\angle3 + m\angle5= 180^{\circ}$$

Step2: Use the definition of congruent angles

$$m\angle4 = m\angle1; m\angle5 = m\angle2$$

Step3: Substitute angles

Substitute \(m\angle4\) with \(m\angle1\) and \(m\angle5\) with \(m\angle2\) in the equation \(m\angle4 + m\angle3 + m\angle5 = 180^{\circ}\)

Answer:

1. \(m\angle4 + m\angle3 + m\angle5= 180^{\circ}\)
2. \(m\angle4 = m\angle1; m\angle5 = m\angle2\)
3. Substitution