If l is parallel to m, find the value of each missing variable
1 answer:
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
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Answer:
The equation to find the answer is .
It has been 5 days since Karen has set her watch.
Step-by-step explanation:
Given:
Karen set her watch 1 second behind
So we will consider;
First term 'a' = 1 second
Also Given :
it falls behind another 2 seconds every day.
So we can consider;
Common difference = 2
We need to find number of days it has been 9 seconds since Karen last set her watch
Solution:
Let number of days be represented by 'n'.
Also Let
Now By Applying formula for Arithmetic Progression we get;
Substituting the given values we get;
Hence The equation to find the answer is .
On Solving the above equation we get;
Subtracting both side by 1 we get;
Now Dividing both side by 2 we get;
Adding 1 on both side we get;
Hence It has been 5 days since Karen has set her watch.