Questions: Find the measures of angle X and angle Y.

Solution Steps

The sum of the interior angles of a quadrilateral is 360°.

Let $x$ and $y$ represent the measure of $\angle X$ and $\angle Y$ respectively. We are given that $\angle Z = 164^\circ$, $\angle V = 102^\circ$, and $\angle W = 90^\circ$. Since the sum of the interior angles of a quadrilateral is $360^\circ$, we have: $x + y + 164^\circ + 102^\circ + 90^\circ= 360^\circ$

$x + y + 356^\circ = 360^\circ$ $x + y = 360^\circ - 356^\circ$ $x + y = 4^\circ$ Since $\angle X$ and $\angle Y$ are marked with the same symbol, they have the same measure. So, $x = y$. Therefore, $x + x = 4^\circ$ $2x = 4^\circ$ $x = 2^\circ$ Since $x = y$, $y = 2^\circ$.

Final Answer