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

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: Recall rhombus angle properties

In a rhombus, opposite angles are equal, consecutive angles are supplementary, and diagonals bisect the angles.

Step2: Calculate $m\angle 2$

Diagonal bisects the angle, so $m\angle 2 = 41^\circ$

Step3: Calculate $m\angle 3$

Consecutive angles sum to $180^\circ$. First find the full angle: $180^\circ - 2\times41^\circ = 98^\circ$, so $m\angle 3 = 98^\circ$

Step4: Calculate $m\angle 1$

Opposite angles are equal, so $m\angle 1 = m\angle 3 = 98^\circ$

Step5: Calculate $m\angle 4$

Diagonal bisects the angle equal to $\angle 3$, so $m\angle 4 = \frac{98^\circ}{2} = 49^\circ$

Answer:

$m\angle 1 = 98^\circ$ $m\angle 2 = 41^\circ$ $m\angle 3 = 98^\circ$ $m\angle 4 = 49^\circ$