Question

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

Answer 1

Answer:

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