In the diagram below of rhombus ABCD, AD congruent AC. Which of the following is the measure of angle BDC?

m<BDC = 30°

Step-by-step explanation:

In a rhombus, each diagonal bisects a pair of opposite angles.

That makes angles ADB and BDC congruent.

Segments AD and AC are congruent, so in triangle ADC, angles ADC and ACD are congruent. Angle ADC is made up of congruent angles ADB and BDC, so m<BDC = (1/2)m<ACD.

In a rhombus, the diagonals are perpendicular. That makes triangle DEC a right triangle with right angle DEC. Then, angles BDC and ACD are complementary.

m<BDC + m<ACD = 90

(1/2)m<ACD + m<ACD = 90

(3/2)m<ACD = 90

m<ACD = 60

m<BDC = (1/2) m<ACD = 60/2 = 30

m<BDC = 30°