Answer:
x = 18
y = 9
Explanation:
A linear pair is two adjacent angles that form a straight line. The sum of the measures of two angles in a linear pair is always 180 degrees.
So,
90 + 2y + 5x - 18 = 180
Simplifying it.
5x + 2y + 72 = 180
5x + 2y = 180 - 72
5x + 2y = 108 ........ [i]
A vertically opposite angle is a pair of angles that are formed when two lines intersect. Vertically opposite angles are always equal.
So,
4x + 2y = 90 ......... [ii]
We can solve this equation by elimination method.
Subtract equation ii from i, we get
4x + 2y - ( 5x + 2y ) = 90 - 108
4x + 2y - 5x - 2y = -18
Simplify like terms:
-x = - 18
Multiply both sides by -1.
x = 18
We can find the value of y by substituting the value of x in the equation [i].
5× (18) + 2y = 108
90 + 2y = 108
Subtract 90 on both sides.
90 + 2y - 90 = 108 - 90
2y = 18
Divide both sides by 2.
y = 9
Therefore, the value of x is 18 and y is 9.