Question

question 7
6.67 pts
consider the quadrilateral lmnp, when lm ∥ np and lp ∥ nm.
what is the value of y?
○ 42
○ 3
○ 6
○ 15

Explanation:

Step1: Identify quadrilateral type

LMNP is a parallelogram (opposite sides parallel). Consecutive angles sum to 180°.

Step2: Find x using ∠L and ∠P

∠L + ∠P = 180°:
$(5x + 12) + (8y + 3x) = 180$ → $8x + 8y + 12 = 180$ → $x + y = 21$...(1)

Step3: Find x using ∠P and ∠N

∠P + ∠N = 180°:
$(8y + 3x) + (3x + 24) = 180$ → $6x + 8y + 24 = 180$ → $3x + 4y = 78$...(2)

Step4: Solve equations (1) and (2)

From (1): $x = 21 - y$. Substitute into (2):
$3(21 - y) + 4y = 78$ → $63 - 3y + 4y = 78$ → $y = 15$

Answer:

15