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What is the Vertex Angle of an Isosceles Triangle Having a Base Angle That is Twice the Vertex Angle?

Answer – The vertex angle of the given isosceles triangle is found to be 36°.

Explanation:

An isosceles triangle is one that has two sides with the same length. The word “isosceles,” in fact, comes via late Latin from the two Greek words isos, meaning “equal,” and skelos, meaning “leg.”

The two sides with the same length are called the legs and converge to form what is called the vertex angle; this angle is opposite the unequal third side that is called the base. The remaining two angles, much like the sides, are equal and are called base angles.

With this information, let’s sketch a rough diagram of the given isosceles triangle.

Isosceles triangle with vertex angle x and base angles of 2x each

Let’s now label the vertex angle we need to find as x. And since each of the base angles is twice the vertex angle, each of them will be 2x.

Further, as the sum of all angles of a triangle is 180°, we can set up the below equation:

$x + 2 x + 2 x = 180 °$

$5 x = 180 °$

$x = \frac{180}{5}$

$x = 36 °$

So the vertex angle A of the given triangle is 36°.

We can also go a step further and solve for the base angle by substituting for x:

$E a c h b a s e a n g l e = 2 x = 2 \times 36 ° = 72 °$

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