Question

in the rhombus, m∠1 = 98. what are m∠2 and m∠3? the diagram is not drawn to scale. none of these m∠2 = 82°, m∠3 = 98° m∠2 = 49°, m∠3 = 82° m∠2 = 49°, m∠3 = 41°

Explanation:

Step1: Recall rhombus properties

In a rhombus, the diagonals are perpendicular bisectors of each other and bisect the angles of the rhombus.

Step2: Find m∠2

Since the diagonal bisects the angle of the rhombus, and m∠1 = 98°, then m∠2=\frac{98^{\circ}}{2}=49^{\circ} as the diagonal bisects the vertex - angle.

Step3: Find m∠3

The diagonals of a rhombus are perpendicular, so in the right - triangle formed by the diagonals, if one non - right angle is m∠2 = 49°, then using the fact that the sum of angles in a triangle is 180°. In a right - triangle with one angle 90° and another m∠2 = 49°, we find m∠3=180^{\circ}-90^{\circ}-49^{\circ}=41^{\circ}.

Answer:

m∠2 = 49°, m∠3 = 41°