Question

1. if m∠e = 53° and m∠f = 46°, determine m∠y.

m∠y = 81°
m∠y = 109°
m∠y = 99°
m∠y = 89°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(z\). So, \(m\angle e+m\angle f + m\angle z=180^{\circ}\).

Step2: Calculate \(m\angle z\)

Substitute \(m\angle e = 53^{\circ}\) and \(m\angle f = 46^{\circ}\) into the equation: \(m\angle z=180^{\circ}-(m\angle e + m\angle f)=180^{\circ}-(53^{\circ}+46^{\circ})=180^{\circ}-99^{\circ}=81^{\circ}\).

Step3: Use linear - pair property

\(\angle y\) and \(\angle z\) form a linear pair. Since the sum of angles in a linear pair is 180°, \(m\angle y = 180^{\circ}-m\angle z\).

Step4: Calculate \(m\angle y\)

Substitute \(m\angle z = 81^{\circ}\) into the equation: \(m\angle y=180^{\circ}-81^{\circ}=99^{\circ}\).

Answer:

\(m\angle y = 99^{\circ}\)