Question

1. four triangles are shown.

images of four triangles with angle measures and an arrow (for exterior angles) and one with w° and z° angles
based on these triangles, which statement is true?

Explanation:

Step1: Recall Triangle Angle Sum

The sum of angles in a triangle is \(180^\circ\), and a linear pair (adjacent angles on a straight line) sums to \(180^\circ\).

Step2: Analyze First Triangle

Right triangle: \(90^\circ + 40^\circ + 50^\circ = 180^\circ\), linear pair: \(50^\circ + 130^\circ = 180^\circ\).

Step3: Analyze Second Triangle

Angles: \(70^\circ + 70^\circ + 40^\circ = 180^\circ\), linear pair: \(40^\circ + 140^\circ = 180^\circ\).

Step4: Analyze Third Triangle

Angles: \(35^\circ + 120^\circ + 25^\circ = 180^\circ\), linear pair: \(25^\circ + 155^\circ = 180^\circ\).

Step5: Analyze Fourth Triangle

Find \(z^\circ\): \(z + 45^\circ + 60^\circ = 180^\circ \implies z = 75^\circ\). Then \(w + z = 180^\circ \implies w = 105^\circ\).

Step6: Generalize

In each triangle, the exterior angle (linear pair with an interior angle) is equal to the sum of the two non - adjacent interior angles (e.g., \(130^\circ = 90^\circ + 40^\circ\), \(140^\circ = 70^\circ + 70^\circ\), \(155^\circ = 35^\circ + 120^\circ\), \(w = 45^\circ + 60^\circ\)). This is the Exterior Angle Theorem.

Answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. (If this was a multiple - choice question with options related to the Exterior Angle Theorem, the correct option would be the one stating this theorem based on the analysis of the triangles.)