Solve for x in an isosceles triangle
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Question 8. Solve for $x$ in the given triangle.
This question includes visual content: The image shows an isosceles triangle. Two of its sides are marked with hash marks, indicating they are of equal length. One of the base angles is labeled 'x', and the vertex angle between the two equal sides is labeled 'x + 30'. By geometric principle, since the triangle is isosceles, the other base angle must also be 'x'.
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In this problem, we need to find the value of x based on the geometry of the triangle provided.
Solving for $x$
Looking at the diagram, notice the hash marks on two sides of the triangle. These markings indicate that the triangle is isosceles, meaning two sides and their opposite angles are equal.
Because the triangle is isosceles, the base angles opposite the congruent sides must be equal. Therefore, the angle on the right side of the base is also x degrees.
Now, we use the fact that the sum of all interior angles in any triangle is always one hundred and eighty degrees.
We can simplify this equation by combining the like terms. We have three terms with x, so that gives us three x.
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