Question

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

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for \(\triangle XYZ\), \(m\angle X + m\angle Y+m\angle Z=180^{\circ}\).

Step2: Substitute the given values

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

Step3: Simplify the left - hand side

\(34^{\circ}+26^{\circ}+m\angle Y=180^{\circ}\), which gives \(60^{\circ}+m\angle Y=180^{\circ}\).

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

Subtract \(60^{\circ}\) from both sides: \(m\angle Y=180^{\circ}-60^{\circ}\).

Answer:

\(m\angle Y = 120^{\circ}\)