Possible Isosceles Triangles

Geometry Level 3

Triangle $ABC$ is isosceles, and $\angle ABC = x^{\circ}.$ For some fixed value of $x$ , the sum of the possible measures of $\angle BAC$ is $240^{\circ}.$

What is $x$ ?

The answer is 20.

1 solution

Anupam Nayak
Feb 4, 2016

There are three cases.

Case 1 : $\angle ABC=\angle ACB$

Case 2 : $\angle BAC=\angle ACB$

Case 3 : $\angle ABC=\angle BAC$

In these cases, we get the sum of the possible values for $\angle BAC$ is-

$\frac{180-x}{2}+180-2x+x=240$

Solving this equation gives $x=20$

I nearly got the answer... just messed up (180-x)/2

Nathael Prolon - 1 year ago

Nice solution1

Lisa Liu - 2 months ago

Possible Isosceles Triangles

The answer is 20.

1 solution

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