Two lines intersect at a point. The angles formed at the intersection are $75^\circ$, $45^\circ$, and $055^\circ$ (which can be read as $55^\circ$). The task is to find the angle denoted by $z$.

GeometryAnglesLinesIntersectionVertical Angles
2025/5/22

1. Problem Description

Two lines intersect at a point. The angles formed at the intersection are 7575^\circ, 4545^\circ, and 055055^\circ (which can be read as 5555^\circ). The task is to find the angle denoted by zz.

2. Solution Steps

When two lines intersect, they form four angles. The sum of the angles around the intersection point is 360360^\circ. Also, vertically opposite angles are equal.
Given angles are 7575^\circ, 4545^\circ and 5555^\circ.
Let's denote the four angles as aa, bb, cc and zz.
Let a=75a = 75^\circ, b=45b = 45^\circ, c=55c = 55^\circ.
Since the sum of the angles around a point is 360360^\circ,
a+b+c+z=360a + b + c + z = 360^\circ
75+45+55+z=36075^\circ + 45^\circ + 55^\circ + z = 360^\circ
175+z=360175^\circ + z = 360^\circ
z=360175z = 360^\circ - 175^\circ
z=185z = 185^\circ

3. Final Answer

The angle zz is 185185^\circ.

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