Question

2. The diagonals AC and BD of a parallelogram ABCD are bisected at the point E. If AE
- 10x find AC if x=3.​

Answer 1

Answer:

60

Step-by-step explanation:

AC=AE+EC

But AE=EC

AC=2AE

AC=2(10X)

AC=2(30)

AC=60

Answer 2

Answer:

Step-by-step explanation:

ABCD is a parallelogram.

Therefore,

AD∥BC

$$\Rightarrow \angle{ACB} = \angle{DAC} = 30°$$

Now, ∠AOB is an exterior angle of △BOC.

As we know that exterior angle is equal to the sum of two interior opposite interior angles.

Therefore,

∠OBC+∠OCB=∠AOB

$$\Rightarrow \angle{OBC} + 30° = 72°$$

$$\Rightarrow \angle{OBC} = 72° - 30° = 42°$$

$$\therefore \angle{DBC} = \angle{OBC} = 42°$$

Hence ∠DBC is $$42°$$.