# Isosceles Triangles - Problem 1

Recall that isosceles triangles are triangles with two congruent sides. So, if given that two sides are congruent, and given the length of one of those sides, you know that the length of the other congruent sides is the same.

Additionally, since isosceles triangles have two congruent sides, they have two congruent angles, as well. Therefore, if the non-congruent angle is known, it is possible to find the value of both of the missing angles, which both have measure y°. By the triangle angle sum theorem, the sum of 2y° (since there are two angles with the same unknown measure) and the third angle is 180°. By adding them together and setting them equal to 180°, solve for y to find the value of the missing angle.

If we apply what we know about isosceles triangles, that is they have two pairs of congruent sides, which means their base angles are congruent, we can solve just about any problem that involves an isosceles triangle.

If we look closely at this, we have two different variables we’re solving for. X, which is this side, so we’re talking about a distance and y which has a degree next to it so we’re talking about the angle. So we’re going split this up into two pieces.

The first piece is the x, the x part is easy. We have these markings here which mean that these two sides must be congruent. Since x is congruent to this side, this side’s distance is 6cm, we can just say that X equals 6 cm, pretty easy.

Next we’re going to have to look at y. Well we know if this is an isosceles triangle, this angle is y as well. So we can say that the triangle angle sum is 180 degrees and that’s equal to 30 plus y plus y. So 180 equals 30 plus, y plus y is 2y, if you remember combining like terms from algebra. So now we have an equation with one variable so we can solve. Subtract 30 from both sides of your equation, 180 minus 30 is 150. So 150 equals 2y. Last step is to divide by two and we see that y equals 75.

Notice I didn’t write degrees here but y is an angle so I’m going to have to write 75 degrees and up here I can write that y is 75 degrees.

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