Question

4 - 2 angles of triangles practice
find the measures of the numbered angles.
$m\angle1 = 90^{\circ}, m\angle2 = 18^{\circ}$
$m\angle1 = 18^{\circ}, m\angle2 = 90^{\circ}$
$m\angle1 = 90^{\circ}, m\angle2 = 28^{\circ}$
$m\angle1 = 28^{\circ}, m\angle2 = 90^{\circ}$

Explanation:

Step1: Identify the right - angle

Since there is a small square at ∠2, by the definition of a right - angle, \(m\angle2 = 90^{\circ}\).

Step2: Use the triangle angle - sum property

In a triangle, the sum of the interior angles is \(180^{\circ}\). For the triangle with angles \(m\angle2\), \(72^{\circ}\), and \(m\angle1\), we have \(m\angle1+72^{\circ}+m\angle2=180^{\circ}\). Substitute \(m\angle2 = 90^{\circ}\) into the equation: \(m\angle1+72^{\circ}+90^{\circ}=180^{\circ}\). Then \(m\angle1=180^{\circ}-(72^{\circ} + 90^{\circ})\). Calculate \(180-(72 + 90)=180 - 162=18^{\circ}\).

Answer:

\(m\angle1 = 18^{\circ}\), \(m\angle2=90^{\circ}\) (the second option)