Question

1. construction a construction square forms a right angle.

if the edges of the board are parallel, find the measures of angles 1, 2, and 3.
$m\angle 1 = ________________^{circ}$
$m\angle 2 = ________________^{circ}$
$m\angle 3 = ________________^{circ}$

Explanation:

Step1: Find \(m\angle1\)

Since the edges of the board are parallel, \(\angle1\) and the \(35^{\circ}\) angle are alternate interior angles.
\(m\angle1 = 35^{\circ}\)

Step2: Find \(m\angle2\)

We know that the construction square forms a right - angle (\(90^{\circ}\)). Using the fact that the sum of angles on a straight line is \(180^{\circ}\), and we have \(35^{\circ}+90^{\circ}+m\angle2 = 180^{\circ}\).

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Step3: Find \(m\angle3\)

Since the edges of the board are parallel, \(\angle3\) and \(\angle2\) are alternate interior angles.
\(m\angle3=m\angle2 = 55^{\circ}\)

Answer:

\(m\angle1 = 35^{\circ}\), \(m\angle2 = 55^{\circ}\), \(m\angle3 = 55^{\circ}\)