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Example Questions
Example Question #72 : Triangles
Which of the following can be the measures of the three angles of an isosceles triangle?
By the Isosceles Triangle Theorem, an isosceles triangle - a triangle with at least two sides of equal length - must have at least two angles of equal degree measure. The choice can therefore be immediately eliminated.
Also, the degree measures must total , so add the measures in each group to find the set that conforms to this condition:
:
:
:
The last group is the correct choice.
Example Question #73 : Triangles
A triangle has one angle measure of degrees and another of degrees. Find the measure of the third angle.
degrees
degrees
degrees
degrees
degrees
degrees
For all triangles, the sum of the three angles is equal to degrees. Therefore, if you are given two angles and you need to solve for the third one, you need to add the two angles you know and subtract that from . Because and because , the third angle has a measure of degrees.
Example Question #74 : Triangles
If one angle of an isosceles triangle measures 120, what are the other two angle measures?
First we need to recall that whenever we add up all 3 angles of any given triangle, the sum will always be .
In an isosceles triangle two of the angles are congruent. Since we are told that one of the angles of our triangle is we know that this is an obtuse triangle, since 120 is greater than 90.
We need to subtract 120 from 180 to find the remainder of the triangle which is
Since we are working with an isosceles triangle, we know that the remaining two angles are going to be congruent. To find the degree of the angles we simply divide 60 by 2. Our answer is; both angles are
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