In rhombus ABCD, angle ABD is 48 find angle C.

A rhombus is a parallelogram in which all sides are equal and the angles are not right.

The diagonals of the rhombus are the bisectors of its catch; therefore, the angle АВД is equal to half of the angle ∠В. Thus:

∠В = ∠АВД ∙ 2;

∠В = 48º ∙ 2 = 96º.

Since opposite angles in a rhombus are equal, and the sum of all its angles is 360º, then:

∠В = ∠Д = 96º;

∠С = ∠А = (360º – ∠В – ∠Д) / 2;

∠С = ∠А = (360º – 96º – 96º) / 2 = 168º / 2 = 84º.

Answer: the angle ∠С is equal to 84º.