If l is parallel to m, find the value of each missing variable

x = 18

y = 5

Step-by-step explanation:

From the figure attached,

'l' and 'm' are the parallel lines and two transversal lines are intersecting these  parallel lines at points A, B and C.

Since, m∠ABC + (7x - 23)° = 180° [Supplementary angles]

m∠ABC = 180° - (7x - 23)°

m∠BCA = (11y - 1)° [Vertical angles]

m∠BAC = 49°

In ΔABC,

m∠ABC + m∠BAC + m∠CAB = 180°

180° - (7x - 23)° + 49° + (11y - 1) = 180°

-7x + 11y = -71

7x - 11y = 71 ------(1)

Since, sum of consecutive angles is 180°

Therefore, m(∠ABC) + (3x + 49)° = 180°

180° - (7x - 23)° + (3x + 49)° = 180°

-4x = -72

x = 18

From equation (1),

7(18) - 11y = 71

11y = 55

y = 5

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation: