Answer:
The value of x is 55 ⇒ 2nd answer
Step-by-step explanation:
* Lets revise the properties of the rhombus
- It has 4 equal sides
- Every two opposite sides are parallel
- Every two opposite angles are equal
- Every two adjacent angles are supplementary (their sum is 180°)
* Now lets solve the problem
- A square divided into two rectangles
- Each rectangle contains a shaded rhombus
- The shaded rhombus has two adjacent angles their measures are
(2x + 20)° and 50°
∵ Every two adjacent angles in the rhombus are supplementary
∵ The sum of the supplementary angles = 180°
∴ The sum of the measures of the angles (2x + 20)° and 50° is 180°
- lets put the equation and solve it to find x
∴ (2x + 20)° + 50° = 180° ⇒ add the like terms
∴ 2x + 70° = 180° ⇒ subtract 70° from both sides
∴ 2x = 110° ⇒ divide both sides by 2
∴ x = 55°
* The value of x is 55
