Question

The measures of the angles of a quadrilateral are: (2x - 4)°, (5x - 10)°, (4x - 8)° and (7x - 14)°. find x.

Answer 1

We know that the sum of all angles of a quadrilateral are 360°  ...(By angle sum property of a quadrilateral)
Thus,
(2x - 4)° + (5x - 10)° + (4x - 8)° + (7x - 14)° = 360°
⇒ Collecting like terms, we get:
(2x + 5x + 4x + 7x) + (-4 -10 - 8 - 14)° = 360°
⇒ 18x - 36° - 360° = 0

⇒ x = `(396°)/(18)`
= 22°.