Find the value of X and Y

x=4, y=10

Step-by-step explanation:

Lines and Angles

When lines cross, the angles formed in the intersections meet certain properties that help us to solve some geometry problems.

We must recall the so-called linear angles, defined as the adjacent angles formed in the point where two lines cross.

Linear angles always add up to 180°

We can see line m intersects with the horizontal (unnamed) line forming two pair of linear angles, thus:

29x - 3 + 15x + 7 = 180

Simplifying:

44x +4 = 180

Subtracting 4:

44x = 176

Dividing by 44:

x = 176/44

x = 4

Now below the horizontal line, we find other pair of linear angles, thus:

13y - 17 + 15x + 7 = 180

Substituting x=4:

13y - 17 + 60 + 7 = 180

Simplifying:

13y + 50 = 180

Subtracting 50:

13y = 180 - 50 = 130

Dividing by 13:

y = 130/13 = 10

y = 10

x=4, y=10