Bunuel wrote:

In the figure above if \(l_1||l_2\), what is the value of x?

A. 70

B. 100

C. 110

D. 150

E. 170

Attachment:

2018-03-16_1010ed.png [ 10.8 KiB | Viewed 284 times ]
A couple of other ways to approach . . .

\(l_1\) and \(l_2\) are cut by a transversal

Alternate interior angles are congruent.

Lower right angle =

\(40°\)Other angle of lower triangle, given =

\(30°\)1) \(x\) = exterior angle

Exterior angle

\(x\) = sum of opposite interior angles of lower triangle

Exterior angle

\(x\) \(= (30° + 40°) =\) \(70°\)OR

2) Straight line: Third angle of lower ∆ +

\(x = 180°\)Interior angles of a triangle sum to 180°

Lower ∆'s third angle =

\(110°\)(\((180° - 30° - 40°) = 110°\) = third angle))

Third angle lies on a straight line with \(x\)

\(110° + x° = 180°\)

\(x = 70°\)

Answer A

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"