Questions: Find the values of (x)

Find the values of (x)
Transcript text: Find the values of $x$
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Solution

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Solution Steps

Step 1: Analyze the figure

The given figure is an isosceles trapezoid. The base angles are marked with $y^\circ$, indicating they are equal. The two non-parallel sides are marked with single hash marks, indicating they are equal in length. The two angles formed between the non-parallel sides and the longer base are marked with $x^\circ$. The sum of the interior angles of a quadrilateral is $360^\circ$. The markings on the sides of the two triangles within the trapezoid indicate they are isosceles. The base angles of the two isosceles triangles are congruent.

Step 2: Set up an equation

The sum of the interior angles of a trapezoid is $360^\circ$. We have two angles measuring $y^\circ$ and two angles measuring $x^\circ$. Therefore, $2x + 2y = 360$.

Step 3: Simplify the equation

Divide both sides of the equation by 2: $x + y = 180$

Final Answer

\\(\boxed{x + y = 180}\\)

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