Question 105662: If the measure of one angle of a triangle is equal to the sum of the measures of the other two angles, then the triangle is always:
(1)acute
(2)obtuse
(3)isoceles
(4)right
EXPLAIN!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! In a triangle the measures of the three angles totals to 180 degrees. Suppose we have
the measures of angles A, B, and C in a triangle and identify these measures as mA, mB, and mC.
Since the total of these three measures is 180 degrees for this triangle, we can write the equation:
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mA + mB + mC = 180
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Now in accordance with the problem we are told that the measure of one of the angles,
say mA, is equal to the sum of the measures of the other two angles ... mB + mC. In equation
form this is:
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mA = mB + mC
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So for mB + mC in the equation for all three angles totaling 180 we can substitute
mA because mA is equal to mB + mC.
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Start with:
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mA + mB + mC = 180
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In place of mB + mC substitute mA to get:
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mA + mA = 180
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Add the terms on the left side to get 2mA and the equation becomes:
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2mA = 180
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Solve for mA by dividing both sides by 2 to reduce the equation to:
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mA = 180/2 = 90 degrees
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Since mA = 90 degrees, the triangle has a right angle and is therefore a right triangle.
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The correct answer from the list of choices is (4) and the explanation is as discussed
above.
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Hope this helps you to understand the problem.
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