Question

Given ABCD, solve for X.

(30 + 5x)" (15+10x)"

A. 13
B. 11
C. 9
D. 7

Answer 1

Answer: C

Explanation: The sum of two angles should be 180, and (30 + 5 • 9) = 75, (15 + 10 • 9) = 105, so both angle adds up to 180.

Answer 2

The value of x of the parallelogram ABCD is 9.

What is a parallelogram?

A parallelogram is a quadrilateral whose opposite sides are parallel and equal in length. The opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.

For the given situation,

Let ABCD be a parallelogram.

The angle of ∠A = (30+5x)° and ∠D = (15+10x)°

According to the property of parallelogram,

The adjacent angles of parallelogram are supplementary,

⇒ $\angle A + \angle D=180$

⇒ $\angle (30+5x) + \angle (15+10x)=180$

⇒ $30+5x+15+10x=180$

⇒ $15x+45=180$

⇒ $15x=180-45$

⇒ $15x=135$

⇒ $x=\frac{135}{15}$

⇒ $x=9$

Hence we can conclude that the value of x of the parallelogram ABCD is 9.

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