Question

Please answer my question

In the adjoining figure, ABCD is a rhombus in which angle BAC = 40°
Find the measures of:
I. Angle ACB
ii. angle ABC
iii. angle ADC
iv. angle ACD
v. angle CAD​

Answer 1

Answer:

Step-by-step explanation:

properties of rhombus : ( which I have used )

• alternate angles equal
• diagonals divides each other into right angles
• all sides are equal
• diagonal bisects the vertex angle
• angles opp. to equal side are equal

AND LET ∠ ABC = ∠ 1; ∠ ACD= ∠ 2; ∠ BCA=∠ 3; ∠ CAD = ∠ 4; ∠ ADC=∠ 5

∠ 2 = 40° ( ALTERNATE ANGLE)

∠ 4 = 40     (diagonal bisects the vertex angle)

IN ΔDOC

∠ 2=40        ∠ DOC = 90 (diagonals divides each other into right angles )

∠ ODC = 180 -(90 +40) = 50

∠ ODC = ∠ ODA = 50       (diagonal bisects the vertex angle)

∠ 5 = 50 +50 = 100    

1) ∠ ACB =∠ 3 =  ∠ 4 = 40    (alternate angle equal)

2) ∠ABC =∠ 1 =  ∠ 5 = 100     (opp. angle of rhombus are equal )

3) ∠ ADC = ∠ 5 = 100

4) ∠ ACD = ∠ 2 =  40  ( ALTERNATE ANGLES EQUAL)

5) ∠ CAD = ∠ 4 = 40

HOPE IT HELP