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

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

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

Answer

Explanation:

Step1: Use rhombus angle property

In a rhombus, consecutive angles are supplementary. $$m\angle 1 + 56^\circ = 180^\circ$$ $$m\angle 1 = 180^\circ - 56^\circ = 124^\circ$$

Step2: Use rhombus diagonal property

Diagonals bisect angles of a rhombus. $$m\angle 2 = \frac{1}{2}m\angle 1 = \frac{1}{2} \times 124^\circ = 62^\circ$$

Step3: Use rhombus diagonal property

Diagonals bisect angles of a rhombus. $$m\angle 3 = \frac{1}{2} \times 56^\circ = 28^\circ$$

Step4: Use triangle angle sum property

The diagonals of a rhombus are perpendicular, so the triangle containing $\angle 4$ has a right angle. $$m\angle 4 + m\angle 3 + 90^\circ = 180^\circ$$ $$m\angle 4 = 180^\circ - 90^\circ - 28^\circ = 62^\circ$$

Answer:

$m\angle 1 = 124^\circ$ $m\angle 2 = 62^\circ$ $m\angle 3 = 28^\circ$ $m\angle 4 = 62^\circ$