Question 480233: Diane draws an obtuse,isosceles triangle with one of the angles measuring 35'. What is the measure of the obtuse angle in her triangle?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! First, let's think about the properties of obtuse triangles. The main feature is that an obtuse triangle has one angle that has a measure greater than 90 degrees. You already know that the sum of the measures of the three angles of a triangle is 180 degrees. Since the measure of the obtuse angle in an obtuse triangle is greater than 90 degrees, there is less than 90 degrees of the whole 180 degrees in the triangle left for the two remaining angles to share.
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Now let's think about what it means to have an isosceles triangle. A key feature of an isosceles triangle is that it has two sides that are equal in length. Another key feature is that the two angles that are opposite of the two equal sides are also equal in their measures.
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What do we also know about the particular obtuse triangle for this problem. We know that the measure of one of the angles is 35 degrees. (You typed 35 and the ' symbol which means minutes, but I'm assuming you meant degrees.)
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35 degrees is obviously not the measure of the obtuse angle, because the measure of the obtuse angle must be greater than 90 degrees. Therefore, 35 degrees must be the measure of one of the two acute (less than 90 degree) angles. And the properties of isosceles triangles (two angles of equal measures) means that the measure of the other acute triangle must also be 35 degrees. This means that the total of the measures of the two acute angles is 35 degrees plus 35 degrees or 70 degrees. The remaining measure in the triangle must be the obtuse angle. This means that the measure of the obtuse angle is 180 degrees minus 70 degrees and it equals 110 degrees.
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So the answer to this problem is that the measure of the obtuse angle is 110 degrees. The measures of the three angles in the triangle for this problem are 35 degrees, 35 degrees, and 110 degrees.
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I hope this helps you to gain some more understanding of the properties of obtuse and isosceles triangles. Good luck.
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