Question

What is the value of x and y in the following figure?

Answer 1

Explanation:

x = 75°

75° + 75° + a = 180°

a + 150° = 180°

a = 180° - 150°

a = 30°

y + 30° = 90°

y = 90° - 30°

y = 60°

I hope I've helped you

Answer 2

`▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪`

The required values are ~

`\boxed{x = 75 \degree}`

and

`\boxed{y = 60 \degree}`

`\large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}`

As it's shown in the figure, the sides opposite to x and Angle 75° are equal. So the corresponding Angles are also equal to one another.

that is ~

• 
  `x = 75 \degree`

I have taken an angle and marked it as " m " in the attachment.

So, according to Angle sum property of a triangle,

• 
  `m + x + 75 \degree = 180 \degree`

• 
  `m + 75 \degree+ 75 \degree= 180 \degree`

• 
  `m + 150 \degree= 180`

• 
  `m = 180 \degree - 150 \degree`

• 
  `m = 30 \degree`

now, it's given that the sum of Angle y and Angle m is 90°

hence,

• 
  `m + y = 90 \degree`

• 
  `30 \degree + y = 90 \degree`

• 
  `y = 90 \degree - 30 \degree`

• 
  `y = 60 \degree`