# Ex: Find the Measure of an Interior Angle of a Triangle

We want to find the measure of each missing interior

angle of the given triangles. Notice our first triangle

is a scalene triangle because all sides are different lengths and therefore, all the angles

have a different measure. Our second triangle is a right triangle, because one of the interior

angles measures 90 degrees. And then finally, the third triangle is an isosceles triangle because two sides have the same length and therefore, the base

angles, or the angles opposite the sides of equal length,

have the same measure. Notice how here they’re

both labeled z degrees. Regardless of the triangle, though, the sum of the interior angles must always be equal to 180 degrees. And we can use this

fact to set up equations and solve for the unknown

angles in each triangle. So looking at our first example, X plus 43 plus 64 must equal 180. Notice how we’re leaving the

degrees off on our equation because we already have a

degree symbol on the variable x. So now we’ll solve this for x, 43 plus 64 equals 107, so we have x plus 107 equals 180 and I will subtract 107 from

both sides to solve for x. So we have x equals 73, which means the missing angle measures 73 degrees. Now for our second example, because we have a right triangle, we can set this up a couple of ways. The sum of the interior

angles must be 180 degrees, but also the two acute

angles of a right triangle are complementary or

have a sum of 90 degrees. Let’s go ahead and set this up two ways. Let’s first use the fact that y plus 53 plus 90 must equal 180. So we have y plus, this

would be 143, equals 180. Subtract 143 on both sides. And we have y equals 180 minus 143 is 37. Therefore, the measure of the

missing angle is 37 degrees. The other option would be to recognize that y plus 53 must equal 90 degrees because these two angles

are complementary. Subtracting 53 on both sides,

we get the same result, y equals 37. And then finally, for

our isosceles triangle, our equation would be z

plus z plus 36 equals 180. Z plus z would be two z. So here we have a two-step

equation to solve, we’d first subtract 36 from both sides, this would give us two z equals 144. And now we solve for z, we

divide both sides by two. So we have z equals 144 divided by two equals 72, and therefore, the two missing angles, which are equal in measure,

both measure 72 degrees. I hope you found this helpful.

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Thank you. Brilliant illustrations and explanations for each triangle type.

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