Question

In a parallelogram ABCD ,angle A=(4x-5) and angle C=(3x+10). find angle A and angle B.

Answer 1

• 
  `\angle A = 55\degree`

• 
  `\angle B = 125\degree`

Explanation:

We know that opposite angles of Parallelogram are equal. From the figure,
`\angle A` and
`\angle C` are the opposite angles i.e they are equal .

`\angle A = \angle C`

`4x - 5 = 3x + 10`

Subtract 3x from both sides,

`x -5 = 10`

Add 5 on both sides,

`x = 15`

`\angle A = 4x - 5`

`\angle A = 4(15) - 5`

`\angle A = 60 - 5 = 55\degree`

Since
`\angle A = \angle C`

`{\boxed{\angle A = 55\degree}}`

`\angle C = 55\degree`

Also,
`\angle A` and
`\angle B` are the adjacent angles whose sum is 180°

`\angle A + \angle B = 180`

`55 + \angle B = 180`

Subtract 55 from both sides,

`\angle B = 180 - 55`

`{\boxed{\angle B = 125\degree}}`

Therefore,

• 
  `\angle A = 55\degree`

• 
  `\angle B = 125\degree`