Question

Three of the interior angles of a polygon are equal to each other The remaining angles are 145, 100 and 115" Find the size of cache of the three equal angles

Answer 1

The size of each of the three equal unknown angles is
`120^(0)`.

Step-by-step explanation:

Let the the unknown angle be represented by x. The polygon is a hexagon, which has three sides and angles.

sum of angle in the hexagon = (n - 2) x
`180^(0)`

n = 6, so that;

Sum of angle in the hexagon = ( 6 - 2) x
`180^(0)`

= 4 x
`180^(0)`

=
`720^(0)`

Therefore;

x + x + x +
`145^(0)` +
`100^(0)` +
`115^(0)` =
`720^(0)`

3x +
`360^(0)` =
`720^(0)`

3x =
`720^(0)` -
`360^(0)`

3x =
`360^(0)`

x =
`120^(0)`

The size of each of the three equal unknown angles is
`120^(0)`.