Question

in $delta xyz$, $yz = 12$, $zx = 18$, and $xy = 7$. which list has the angles of $delta xyz$ in order from largest to smallest? answer: $mangle y$, $mangle x$, $mangle z$; $mangle z$, $mangle y$, $mangle x$; $mangle z$, $mangle x$, $mangle y$; $mangle y$, $mangle z$, $mangle x$; $mangle x$, $mangle z$, $mangle y$; $mangle x$, $mangle y$, $mangle z$

Explanation:

Step1: Recall angle - side relationship

In a triangle, the largest angle is opposite the longest side and the smallest angle is opposite the shortest side.

Step2: Identify side lengths

Given \(YZ = 12\), \(ZX=18\), \(XY = 7\). The order of side - lengths from longest to shortest is \(ZX>YZ>XY\).

Step3: Determine angle order

The angle opposite \(ZX\) is \(\angle Y\), the angle opposite \(YZ\) is \(\angle X\), and the angle opposite \(XY\) is \(\angle Z\). So the order of angles from largest to smallest is \(m\angle Z\), \(m\angle Y\), \(m\angle X\).

Answer:

C. \(m\angle Z\), \(m\angle Y\), \(m\angle X\)