Question

In a parallelogram ABCD, one angle is 28 more than thrice of its adjacent angle. Find the
angles of the parallelogram​

Answer 1

Given

✭ ABCD is a parallelogram

✭ One angle is 28 more then thrice of its adjacent angle

To Find

◈ Angles of the parallelogram

Solution

Concept

In a parallelogram adjacent angles add up to 180°

━━━━━━━━━

☯ As Per the Question

So given that an adjacent angle is 28 more than thrice it's adjacent angles and so as they add up to 180° we shall assume the angles as,

• x
• x180-x

So now,

➝ x = 28+3(180-x)

➝ x = 28+540-3x

➝ x = 568-3x

➝ x+3x = 568

➝ 4x = 568

➝ x = 568/4

➝ x = 142

So now the Angles will be,

➳ Angle¹ = x = 142°

➳ Angle² = 180-x = 180-142 = 38°

In a parallelogram opposite angles are equal so then the angles of the parallelogram will be 142°,38°,142°,38°

❍ Parallelogram

⪼ Opposite sides are equal and parallel

⪼ Opposite angles are equal

⪼ Adjacent angles add up to 180°

⪼ Add the angles add up to 360°

━━━━━━━━━━━━━━━━━━