Question

fill in the missing steps of the proof of the exterior angle of a triangle corollary. given: △abc with ∠1 an exterior angle. prove: m∠1=m∠2 + m∠3. 1. ∠1 is an exterior angle. statements 1. given 2. m∠1 + m∠4 = 180°. reasons

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of $\triangle ABC$ is $m\angle2 + m\angle3+m\angle4=180^{\circ}$ (by the Angle - Sum Property of a Triangle).

Step2: Recall linear - pair property

$\angle1$ and $\angle4$ form a linear pair. So, $m\angle1 + m\angle4=180^{\circ}$ (by the Linear - Pair Postulate).

Step3: Substitute and prove

Since $m\angle2 + m\angle3+m\angle4 = 180^{\circ}$ and $m\angle1 + m\angle4=180^{\circ}$, we can substitute.
$m\angle2 + m\angle3+m\angle4=m\angle1 + m\angle4$.
Subtracting $m\angle4$ from both sides of the equation, we get $m\angle1=m\angle2 + m\angle3$.

Answer:

1. Given: $\angle1$ is an exterior angle of $\triangle ABC$.

• Reason: Given.

1. $m\angle2 + m\angle3+m\angle4 = 180^{\circ}$

• Reason: Angle - Sum Property of a Triangle.

1. $m\angle1 + m\angle4=180^{\circ}$

• Reason: Linear - Pair Postulate.

1. $m\angle2 + m\angle3+m\angle4=m\angle1 + m\angle4$

• Reason: Substitution Property of Equality.

1. $m\angle1=m\angle2 + m\angle3$

• Reason: Subtraction Property of Equality.