Question

if ( mangle x = 34^circ ) and ( mangle z = 26^circ ), what is ( mangle y )?
( \bigcirc ) ( mangle y = 26^circ )
( \bigcirc ) ( mangle y = 34^circ )
( \bigcirc ) ( mangle y = 60^circ )
( \bigcirc ) ( mangle y = 120^circ )

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle X + m\angle Z + m\angle Y = 180^\circ\).

Step2: Substitute known values

We know \(m\angle X = 34^\circ\) and \(m\angle Z = 26^\circ\). Substitute these into the formula: \(34^\circ + 26^\circ + m\angle Y = 180^\circ\).

Step3: Calculate sum of known angles

First, add \(34^\circ\) and \(26^\circ\): \(34^\circ + 26^\circ = 60^\circ\).

Step4: Solve for \(m\angle Y\)

Now, we have \(60^\circ + m\angle Y = 180^\circ\). Subtract \(60^\circ\) from both sides: \(m\angle Y = 180^\circ - 60^\circ = 120^\circ\).

Answer:

\(m\angle Y = 120^\circ\) (the option: \(m\angle Y = 120^\circ\))