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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
​

Sagot :

mhanifa

Answer:

  • See below

Step-by-step 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)
View image mhanifa
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