Answer:
x = 43
y = 94
Explanation:
The Vertical Angle Theorem states that when two straight lines intersect, the pairs of vertical angles formed are congruent. In other words, if two lines intersect at a point, the angles opposite each other at that intersection point have equal measures.
Value of x
From observation of the given diagram, angle 2x° is vertically opposite angle 86°. Therefore, to find the value of x, equate the two angles and solve for x:
2x° = 86°
2x = 86
2x ÷ 2 = 86 ÷ 2
x = 43
Value of y
Angle K and angle 86° form a straight line. As angles on a straight line sum to 180°, then:
K + 86° = 180°
Solve for K:
K + 86° - 86° = 180° - 86°
K = 94°
Angle y is vertically opposite angle K. Therefore, to find the value of y, equate the two angles and solve for y:
y° = K
y° = 94°
y = 94