Question

Find the value of the unknown angle X.

158°
51°
21°
The diagram is not drawn to scale.
O
2 =
O

Answer 1

x =
`130^(o)`

Explanation:

The given figure is a trapezium which is a quadrilateral with four sides.

But,

Sum of angles in a quadrilateral = (n - 2) x 180

where n is the number of sides.

For a quadrilateral, n = 4. So that,

Sum of angles in a quadrilateral = (4 - 2) x 180

= 2 x 180

=
`360^(o)`

The sum of angles in a quadrilateral is
`360^(o)`.

Thus,

`158^(o)` +
`51^(o)` +
`x^(o)` +
`21^(o)` =
`360^(o)`

`x^(o)` +
`230^(o)` =
`360^(o)`

`x^(o)` =
`360^(o)` -
`230^(o)`

=
`130^(o)`

The value of x is
`130^(o)`.