Question

geometry
find the measurement of the exterior angle.

in the image below, new path and east path are parallel. find the measure of:

Explanation:

Step1: Find the exterior angle of the first triangle

Use the exterior angle theorem: the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
For the first triangle with interior angles \(73^{\circ}\) and \(62^{\circ}\), the exterior angle \(z\) is \(73 + 62\).

$$z=73 + 62=135^{\circ}$$

Step2: Find angle \(y\)

Since \(y\) and \(47^{\circ}\) are vertical angles (opposite angles formed by the intersection of two lines), \(y = 47^{\circ}\) (vertical angles are equal).

Step3: Find angle \(z\) (another way - using the second part of the problem)

In the second figure, for the triangle with angle \(72^{\circ}\) and \(y = 47^{\circ}\), if we consider the relationship with parallel lines (alternate interior angles etc. are not needed here as we can use triangle angle - sum or exterior angle). But since we already found \(z = 135^{\circ}\) from the first triangle (and if we assume the first problem is the main one). For the second figure:

• For angle \(x\): Using the property of parallel lines (alternate interior angles if we assume a transversal), but if we consider the triangle - related approach (assuming the first problem is the one to solve as the second has multiple variables and the first is a single - variable exterior angle problem).

If we consider the first problem (the triangle with \(73^{\circ}\), \(62^{\circ}\) and exterior angle \(z\)):

Answer:

\(135^{\circ}\)