Question

find the values of x, y, and z. the diagram is not to scale.

x = 63, y = 104, z = 76
x = 63, y = 76, z = 104
x = 76, y = 63, z = 104
x = 76, y = 104, z = 63

Explanation:

Step1: Find x using angle - sum property of a triangle

In the left - hand triangle, the sum of interior angles of a triangle is 180°. So, \(x=180-(46 + 58)=180 - 104=76\).

Step2: Find z

The non - labeled angle adjacent to z in the right - hand triangle is \(180-(x + 13)\). Since \(x = 76\), this angle is \(180-(76+13)=91\). Then, \(z = 180 - 91=104\).

Step3: Find y

Since \(y+z = 180\) (linear pair of angles), and \(z = 104\), then \(y=180 - 104 = 76\).

Answer:

\(x = 76,y = 76,z = 104\), so the correct option is \(x = 76,y = 76,z = 104\) (the second option in the multiple - choice list).