Question

1. describe the error in finding m∠1.

x
m∠1 + 80° + 50° = 180°
m∠1 + 130° = 180°
m∠1 = 50°

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180°. But ∠1 is an exterior angle.

Step2: Identify correct property

The exterior - angle property states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m\angle1=80^{\circ}+50^{\circ}\).

Step3: Analyze error

The error is using the interior - angle sum formula for an exterior angle. The equation \(m\angle1 + 80^{\circ}+50^{\circ}=180^{\circ}\) is incorrect as ∠1 is not an interior angle of the triangle.

Answer:

The error is using the interior - angle sum formula of a triangle (\(180^{\circ}\) for the sum of interior angles) for an exterior angle. The correct formula for an exterior angle of a triangle is that it equals the sum of the two non - adjacent interior angles, not the sum of all three interior angles with it included.