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
Answers
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°
#answerwithquality
#BAL
Answer:
angle CAB= 40 DEGREE
angle BCD= 80 DEGREE
angle ADC= 100 DEGREE