Question

use the figure shown.
select all the true statements.
$x = y$
$x + y = 180$
$y = z$
$x + z = 180$
$y + z = 180$

Explanation:

Step1: Find the value of \(x\)

Use the triangle angle - sum property. The sum of angles in a triangle is \(180^{\circ}\).
So, \(x = 180-(82 + 54)\)
\(x=180 - 136\)
\(x = 44^{\circ}\)

Step2: Analyze \(x + y=180\)

Since \(x\) and \(y\) are adjacent angles forming a linear pair.
By the linear - pair postulate, \(x + y=180^{\circ}\) (True)

Step3: Analyze \(y = z\)

\(y\) and \(z\) are vertical angles.
By the vertical - angles theorem, \(y = z\) (True)

Step4: Analyze \(x + z=180\)

Since \(x + y=180\) and \(y = z\), substituting \(y\) with \(z\) gives \(x+z = 180^{\circ}\) (True)

Answer:

\(x + y=180\), \(y = z\), \(x + z=180\)