The smaller diagonal of the rhombus is 8 cm and the obtuse angle is 120 degrees. find the perimeter of the diamond.

1. The vertices of the rhombus – A, B, C, D. ∠B = 120 °. BD = 8 centimeters. P is the perimeter of the rhombus.

2. Diagonal ВD is a bisector (according to the properties of a rhombus) and divides ∠В and ∠D into two equal angles:

∠ABD = ∠ADB = 120 °: 2 = 60 °.

3.∠А = 180 ° – (∠АВD + ∠АDВ) = 180 ° – 120 ° = 60 °. The angles of triangle ABD are equal.

Hence, its sides are also the same length:

AB = AD = BD = 8 centimeters.

AB and AD are the sides of the rhombus. This means that the length of each of its four sides is 8 centimeters.

4. P = 8 x 4 = 32 centimeters.