Question

4 - 2 angles of triangles practice
find the measures of the numbered angles.
$m\angle1 = 15^{\circ},m\angle2 = 35^{\circ},m\angle3 = 115^{\circ}$
$m\angle1 = 125^{\circ},m\angle2 = 55^{\circ},m\angle3 = 90^{\circ}$
$m\angle1 = 125^{\circ},m\angle2 = 55^{\circ},m\angle3 = 95^{\circ}$
$m\angle1 = 55^{\circ},m\angle2 = 125^{\circ},m\angle3 = 90^{\circ}$

Explanation:

Step1: Find \(m\angle1\)

Use the angle - sum property of a triangle. The sum of angles in a triangle is \(180^{\circ}\). In the left - hand triangle, if two angles are \(70^{\circ}\) and \(55^{\circ}\), then the non - adjacent interior angle to \(\angle1\) is \(180^{\circ}-(70^{\circ} + 55^{\circ})=55^{\circ}\). Also, \(\angle1\) and the non - adjacent interior angle form a linear pair. So, \(m\angle1=180^{\circ}-55^{\circ}=125^{\circ}\).

Step2: Find \(m\angle2\)

\(\angle2\) and the \(55^{\circ}\) angle are vertical angles. Vertical angles are equal. So, \(m\angle2 = 55^{\circ}\).

Step3: Find the angle adjacent to \(150^{\circ}\)

The angle adjacent to \(150^{\circ}\) is \(180^{\circ}-150^{\circ}=30^{\circ}\) (linear - pair property).

Step4: Find \(m\angle3\)

Use the angle - sum property of a triangle for the right - hand triangle. Let the angles of the right - hand triangle be \(m\angle2 = 55^{\circ}\), the angle adjacent to \(150^{\circ}\) (\(30^{\circ}\)), and \(m\angle3\). Then \(m\angle3=180^{\circ}-(55^{\circ}+30^{\circ})=95^{\circ}\).

Answer:

\(m\angle1 = 125^{\circ},m\angle2 = 55^{\circ},m\angle3 = 95^{\circ}\) (the third option)