Question

In the adjoining figure, ABCD is a rhombus and ∠ABD = 50° . Find: i) ∠CAB ii) ∠BCD iii) ∠ADC​

Answer 1

Answer:

Angles of a Rhombus

Answer: On Summarizing our findings we get

1. ∠ CAB = 40° and

2.∠BCD = 80°

3.∠ADC = 100°

Explanation:

Given that ABCD is a RHOMBUS

and ∠ABD = 50°

Need to determine ∠CAB , ∠BCD and ∠ADC

One of the important property of RHOMBUS IS DIAGONAL OF THE RHOMBUS BISECTS OPPOSITE ANGLES.

⇒ ∠ABD = ∠DBC = (1/2)∠ABC = 50° and

also ∠ CAB = (1/2)∠DAB   ---------eq(1)

As (1/2)∠ABC = 50°

⇒ ∠ABC = 50° × 2 = 100°

since OPPOSITE ANGLES OF RHOMBUS ARE EQUAL

⇒ ∠ADC = ∠ABC = 100°

⇒ ∠ADC = 100°

And also CONSECUTIVE ANGLES OF RHOMBUS WHICH IS A KIND OF PARALLEOGRAM ARE SUPPLEMETARY

⇒ ∠ADC  + ∠BCD = 180°

⇒ 100° + ∠BCD = 180°       [ Since ∠ADC = 100° ]

⇒ ∠BCD = 180° - 100° = 80°

⇒ ∠BCD = 80°

⇒ ∠DAB  = ∠BCD = 80°     [ opposite angles of Rhombus are equal ]

⇒∠DAB  =  80°

from eq (1) ∠ CAB = (1/2)∠DAB   = (1/2)×80° = 40°

⇒ ∠ CAB = 40°

On Summarizing our findings we get

1. ∠ CAB = 40° and

2.∠BCD = 80°

3.∠ADC = 100°