Question

In the adjoining figure ABCD is a rhombus and angle abd is equal to 50 degree. find

1.angle CAB
2.angle BCD
3.angle ADC
​

Answer 1

• See below

Explanation:

Property of the rhombus:

• Opposite angles are congruent and adjacent angles are supplementary.
• Diagonals are angle bisectors.
• Diagonals are perpendicular.

We have:

• m∠ABD = 50°

Angle ABC is:

• m∠ABC = 2*m∠ABD = 50°*2 = 100°

Opposite angle is equal to this:

• m∠ADC = m∠ABC = 100°

Adjacent angles are:

• m∠BAD = m∠BCD = 180° - 100° = 80°

The missing angles measures:

• 1) m∠CAB = 1/2*m∠BAD = 1/2*80° = 40°
• 2) m∠BCD = 80° (shown above)
• 3) m∠ADC = 100° (shown above)