The missing values are: a. BC = 6; b. m∠ADC = 60°; c. m∠DCB = 120°; d. m∠AXB = 90°; e. m∠1 = 60° f. m∠2 = 60°; g. m∠3 = 30°; h. m∠4 = 30°; i. AX = 3; j. Triangle ABC is an isosceles triangle.
What is a rhombus?
A rhombus is a four-sided polygon with all sides of equal length, featuring parallel opposite sides and equal opposite angles. Also, in a rhombus, the opposite angles are congruent, the two diagonals intersect at a right angle and divide each other into equal halves at 90°, and adjacent angles together form a sum of 180°.
Using the above properties of a rhombus, we can find the missing values as explained below:
a. BC = AB,
AB is given as 6
So, BC = 6
b. m∠ADC + m∠DAB = 180° [adjacent angles]
m∠ADC = 180 - m∠DAB
m∠ADC = 180 - 120
m∠ADC = 60°
c. m∠DCB = m∠DAB [opposite angles]
m∠DCB = 120°
d. m∠AXB = 90° [right angle]
e. m∠1 = 1/2(120) = 60° [diagonals bisect the angles]
f. m∠2 = 60°
g. m∠3 = 180 - 90 - 60
m∠3 = 30°
h. m∠4 = m∠3 = 30°
i. AX = XC
AX = 3
j. Triangle ABC is an isosceles triangle because side AB = BC.