Question

using parallel lines find ( mangle 1 ) and ( mangle 2 ). explain your reasoning. (review 3.3 for 4.4) 43.

Explanation:

Step1: Find \( m\angle1 \)

Since the two lines are perpendicular, \( m\angle1 = 90^{\circ} \) (by the definition of perpendicular lines forming right angles).

Step2: Find \( m\angle2 \)

The sum of angles around a point on a straight line is \( 180^{\circ} \). Given one angle is \( 90^{\circ} \) (from the perpendicular lines) and \( \angle1 = 90^{\circ} \), but looking at the vertical/adjacent relationships. Wait, actually, using the property that the lines are perpendicular and the other line - the horizontal lines are parallel. Wait no, the key is that the two lines (vertical and horizontal) are perpendicular. So \( \angle1 \) is formed by perpendicular lines: \( m\angle1=90^{\circ} \). For \( \angle2 \), since the lines are perpendicular and using the fact that \( \angle2 \) and the \( 90^{\circ} \) angle (from the perpendicular intersection) and another right - angle - related property (alternate way: the sum of angles in a quadrant - like section). Wait, more simply, since the two lines are perpendicular (the vertical and horizontal), \( \angle1 = 90^{\circ} \). And \( \angle2 \) is equal to \( 90^{\circ} \) as well because of the vertical - angle relationship (the angles opposite each other when two lines intersect are equal). But wait, no, actually, looking at the figure (assuming standard perpendicular intersection where the other horizontal line is parallel - but no, the key is that the vertical line is intersected by two horizontal lines (parallel, but the main intersection is the perpendicular one). Wait, no - re - evaluating. The two lines (one vertical, one horizontal) intersect at \( \angle1 \), forming a right angle (\( 90^{\circ} \)). Then \( \angle2 \) and the \( 90^{\circ} \) angle (from the lower perpendicular intersection) - no, wait, actually, using the property of vertical angles. When two lines intersect, vertical angles are equal. But here, the vertical line and the horizontal line intersect: \( \angle1 \) is \( 90^{\circ} \) (perpendicular). Then \( \angle2 \) is also \( 90^{\circ} \) because the lines are perpendicular (all four angles formed by perpendicular lines are \( 90^{\circ} \)).

Answer:

\( m\angle1 = 90^{\circ}\) and \( m\angle2=90^{\circ}\) because the lines are perpendicular, and all angles formed by perpendicular lines are right angles (\( 90^{\circ}\)).