In the figure above (not drawn to scale), the lines L and P are parall

Answer = C. 34

Refer diagram below:



There sum has to be 180

3x+3+2x+7 = 180

x = 34

Sum of the given 2 angles is 180 degree as it is a parallelogram.

Hence 3x + 3 +2x+7=180 ==> x=34. hence answer c.

OFFICIAL SOLUTION:

(C) There are two bits of information that the reader must be familiar with before undertaking this problem. The first is to be comfortable solving systems of linear equations; and, the second is to know some things about parallel lines and transversals (lines that cut through parallel lines).

Essentially, there are two angles at play here (no pun intended). The first is that angles that are on alternate interior sides of the transversal (angles like BAD and ADP) are equal. And, angles that are on the same side are supplementary. As you know supplementary angles are angles whose sum is equal to 180°. We can set up and solve the following equation for x: (3x + 3) + (2x + 7) = 180. We can reduce this equation by combining like terms and rewrite it as: 5x = 170. Clearly, we can reason that x = 34, or answer choice (C).

quadrilateral ABCD is actually a parallelogram as it lies between a pair of parallel lines
\(\angle\) BAD and \(\angle\) ABC are supplementary
supplementary angles means a total of \(180^{\circ}\)
so \((3x+3)\) + \((2x+7)\) = 180
\(5x\)=180 - 10
\(x\) = 34
correct answer - C

\(3x + 3 + 2x + 7 = 180\)

Or, \(5x = 170\)

Or, \(x = 34\), ANswer is (C)