for the rhombus below, find the measures of $\\angle 1$, $\\angle 2$, $\\angle 3$, and $\\angle 4$.\n$m…

for the rhombus below, find the measures of $\\angle 1$, $\\angle 2$, $\\angle 3$, and $\\angle 4$.\n$m \\angle 1 = \\square^{\\circ}$\n$m \\angle 2 = \\square^{\\circ}$\n$m \\angle 3 = \\square^{\\circ}$\n$m \\angle 4 = \\square^{\\circ}$

for the rhombus below, find the measures of $\\angle 1$, $\\angle 2$, $\\angle 3$, and $\\angle 4$.\n$m \\angle 1 = \\square^{\\circ}$\n$m \\angle 2 = \\square^{\\circ}$\n$m \\angle 3 = \\square^{\\circ}$\n$m \\angle 4 = \\square^{\\circ}$

Answer

Explanation:

Step1: Identify angle 2 using rhombus properties

In a rhombus, diagonals bisect the vertex angles. $$m\angle 2 = 44^{\circ}$$

Step2: Identify angle 4 using parallel lines

Opposite sides are parallel; alternate interior angles are equal. $$m\angle 4 = m\angle 2 = 44^{\circ}$$

Step3: Calculate angle 3 using triangle properties

Rhombus sides are equal, forming an isosceles triangle. $$m\angle 3 = 180^{\circ} - (44^{\circ} + 44^{\circ}) = 92^{\circ}$$

Step4: Identify angle 1 using opposite angles

Opposite angles in a rhombus are equal. $$m\angle 1 = m\angle 3 = 92^{\circ}$$

Answer:

$m\angle 1 = 92^{\circ}$ $m\angle 2 = 44^{\circ}$ $m\angle 3 = 92^{\circ}$ $m\angle 4 = 44^{\circ}$