Question

the angels of a parallelogram ABCD are in the ratio of 1:4:1:4. Find all the four angles.
please explain it ​

Answer 1

Given:

• Ratio of angles of parallelogram ABCD = 1:4:1:4

To find:

• All the four angles of the parallelogram.

Solution:

• Let the first angle be 4x. (∠A)
• Let the second angle be x. (∠B)
• Let the third angle be 4x. (∠C) [Opposite angles of a parallelogram are equal]
• Let the fourth angle be x. (∠D) [Opposite angles of a parallelogram are equal]

We know that sum of all angles of a quadrilateral is 360°.

So,

∠A + ∠B + ∠C + ∠D = 360°

4x + x + 4x + x = 360°

2(4x+x) = 360°

2×5x = 360°

10x = 360°

$\sf {x = \dfrac {360}{10}}$

$\dag {\boxed {\mathfrak {\blue {x = 36 \degree}}}}$

Verification:

Substitute the value of x as 36 in the equation,

4x + x + 4x + x = 360°

4×36 + 36 + 4×36 + 36 = 360°

144 + 36 + 144 + 36 = 360°

288 + 36 + 36 = 360°

288 + 72 = 360°

360° = 360°

LHS = RHS

Hence Verified!

The angles are:

• First angle (∠A) = 4x

= (4×36)°

= 144°

• Second angle (∠B) = x

= 36°

• Third angle (∠C) = 4x

= (4×36)°

= 144°

• Fourth angle (∠D) = x

= 36°

The angles of the parallelogram are 144°, 36°, 144° and 36°.