Option D) 11 is the value of x.
Explanation:
The given figure ABCD is a parallelogram.
To find the x value, solve the given angles based on the properties of parallelogram.
The two main properties of parallelogram based on their angles are :
- The opposite angels of the parallelogram are congruent which has same measure of angle.
- The consecutive angles are of the parallelogram are supplementary which is equal to 180°.
In the given figure ABCD,
The angle B and angle D are opposite angles and has same measure.
Similarly, angle C and angle A are opposite angles and has same measure.
The angle A and angle B are consecutive angles that equals to 180 degree.
Similarly, angle C and angle D are consecutive angles that equals to 180°.
To Solve for x :
We already know that, both the angles A and B are consecutive angles.
Therefore, their sum is equal to 180 degree.
⇒ angle A + angle B = 180
⇒ (8x+30) + (4x+18) = 180
⇒ 12x + 48 = 180
⇒ 12x = 180 - 48
⇒ 12x = 132
Divide by 12 on both sides,
⇒ x = 132 ÷ 12
⇒ x = 11
∴ Option D) 11 is the value of x.