Question

Please explain how you get your answer so i get a better understanding of this...

Using the image below, if I is parallel to M, find the value of y.


(im really struggling with this question so please do explain your answering.)

Answer 1

16.11 (appx.)

Explanation:

since l and m are parallel and a line intersects them, so we can say that the line is the transversal. from the figure we see that

7x + 12 = 12x - 28 [they are internal alternate angles and alternate angles are always equal to one another]

now, we can find the value of x from the equation

12x - 7x = 28 + 12

⇒ 5x = 40

⇒ x = 8

so the angle (7x+12)° is ((7*8)+12) = 68°

so (12x-28)° is also equal to 68° [cause of being alternate angles]

now, look at the figure,

angle (9y-77)° & (12x-28)° add upto a straight line as in 180°

and we know (12x-28)° = 68°

so now,

9y-77 = 68

⇒9y = 68+77

⇒9y = 145

⇒y = 16.11 (appx.)