Question

7. find all the angles of parallelogram
ABCD, if angle A
is two-third of a right angle.​

Answer 1

Step-by-step explanation:

Given:

• ∠A is two third of a right angle.

To Find:

• What is the meaure of all angles ?

Solution: Let ABCD be a parallelogram and measure of ∠B is x°.

• ∠A = ∠C (Opposite ∠s of ||gm are equal)
• ∠B = ∠D = x (Opposite angles equal)
• AB || DC and AD || BC (Opposite sides of ||gm are parallel)

Now, ∠A is the 2/3 times of right angle.

➨ ∠A = 2/3 $\times$ 90

➨ ∠A = 2 $\times$ 30 = 60°

So, ∠A = ∠C = 60°

As we know that

★ Sum of all angles of ||gm = 360° ★

$\implies{\rm }$ ∠A + ∠B + ∠C + ∠D = 360°

$\implies{\rm }$ 60° + x° + 60° + x° = 360°

$\implies{\rm }$ 120° + 2x° = 360°

$\implies{\rm }$ 2x° = 360° – 120°

$\implies{\rm }$ x = 240°/2

$\implies{\rm }$ x = 120°

Hence,

➮ ∠B = ∠D = x = 120° ( Each )

So final values of all angles are

• ∠A = 60°

• ∠B = 120°

• ∠C = 60°

• ∠D = 120°