Question

(x+10)°+(2x+20)°=180°. For what value of X is the quadrilateral a parallelogram?​

Answer 1

Answer: X = 50

Step-by-step explanation: We shall first solve for X in the algebraic expression as follows ;

(X + 10) + (2X + 20) = 180

By removing brackets and collecting like terms we now have

X + 2X + 10 + 20 = 180

3X + 30 = 180

Subtract 30 from both sides of the equation

3X = 150

X = 50

If X has been identified as equal to 50, then the two angles given shall be

Angle 1 = X + 10

Angle 1 = 50 + 10

Angle 1 = 60

Also

Angle 2= 2X + 20

Angle 2 = 2(50) + 20

Angle 2 = 100 + 20

Angle 2 = 120

One of the properties of a parallelogram is, “Opposite angles are congruent.”

The other two angles would also measure 60 and 120, and the sum of all the interior angles shall be;

60 + 120 + 60 + 120 = 360

360 = 360.