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ISEE Middle Level
Mathematics Achievement

Finding Angle in Parallel Lines with a Transversal

Very Hard Geometry Lines And Angles

In the diagram below, we have two parallel lines, line $l_1$ and line $l_2$, and a transversal line $t$ that intersects these two parallel lines at points $A$ and $B$. The angle formed between line $l_1$ and line $t$ at point $A$ is denoted as angle $1$, and measures $x$ degrees. Angle $2$, formed at point $B$ between line $l_2$ and line $t$, is equal to the supplementary angle of angle $1$. If angle $3$ is formed at the intersection of line $t$ and a vertical line that intersects $l_2$ such that angle $3$ is also equal to the sum of angles $1$ and $2$. What is the value of $x$?

Hint

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