Question

Quadrilateral ABCD is a rhombus. if the measure of ADC equals 60°, then the measure pf EDC equals?​

Answer 1

In a rhombus ABCD with ∠ADC measuring 60°, the diagonals being perpendicular bisectors make △ADC and △EDC isosceles, and since ADC is an equilateral triangle, the measure of ∠EDC also equals 60°.

Step-by-step explanation:

If quadrilateral ABCD is a rhombus and the measure of ∠ADC equals 60°, then the measure of ∠EDC can be determined using the properties of rhombuses and triangles. In a rhombus, all sides are of equal length, which means △ADC and △EDC are isosceles triangles. Furthermore, the diagonals of a rhombus are perpendicular bisectors of each other, which means they bisect the angles at the vertices they connect.

Since ∠ADC is 60° and AD is a diagonal that bisects ∠A, △ADC is an equilateral triangle (all angles are 60°) and AD bisects ∠A, implying ∠AD is also 60°. By the properties of a rhombus, this also means that ∠EDC is 60° because it is the angle bisected by the other diagonal.

Therefore, the measure of ∠EDC equals 60°.

Answer 2

60 divided by 2 = 30

We half it because Angle E halfs Angle D

Step-by-step explanation:

As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; as with a parallelogram, the angles of opposite pairs of vertices are equal, and the sum of the angles of two adjacent vertices is 180 degrees.