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: Use the triangle - angle sum theorem

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

Step2: Substitute the given values

We know that \(m\angle X = 34^{\circ}\) and \(m\angle Z = 26^{\circ}\). Substituting these into the equation \(m\angle X + m\angle Y+m\angle Z=180^{\circ}\), we get \(34^{\circ}+m\angle Y + 26^{\circ}=180^{\circ}\).

Step3: Simplify the left - hand side

First, add \(34^{\circ}\) and \(26^{\circ}\): \(34^{\circ}+26^{\circ}=60^{\circ}\). So the equation becomes \(60^{\circ}+m\angle Y=180^{\circ}\).

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

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

Answer:

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