Question 117645: find the measure of each base angle of an isosceles triangle if the vertex angle measures 76 degrees
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The sum of the angles of a triangle are 180 degrees.
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If the vertex angle of the triangle is 76 degrees, that means that the two angles that remain
must result in a total of 180 degrees when they are added to 76 degrees. Think of it this
way in equation form: if the three angles of a triangle are A, B, and C, then
their measures
add to 180 degrees as follows:
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mA + mB + mC = 180
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where mA represents the measure of angle A, mB the measure of angle B, and mC the measure of
angle C.
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In this problem you are told that the measure of one of the angles (let's say mA) is 76
degrees. In the equation for the sum of the angles, we substitute 76 for mA to get:
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76 + mB + mC = 180
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We get rid of the 76 on the left side by subtracting 76 from both sides to get:
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mB + mC = 180 - 76 = 104
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So the equation has simplified to:
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mB + mC = 104
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Now think in terms of isosceles triangles. The unique things about isosceles triangles are
that two of the sides have the same lengths, and the measures of the two base angles are
also equal.
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Therefore, regarding the two base angles we know mB = mC. So we can substitute mB for mC in
our equation. When we make that substitution we get:
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mB + mB = 104
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Adding the two terms on the right side results in:
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2*mB = 104
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We can solve for mB by dividing both sides of this equation by 2 and we get:
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mB = 104/2 = 52 degrees
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Since the measure of one base angle equals 52 degrees we know that the measure of the other
base angle also equals 52 degrees.
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So in the given triangle the measures of the three angles are 52 degrees, 52 degrees, and
76 degrees. The total of these 3 measures is 180 degrees, just as it must be.
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Hope this helps you to understand the problem and how to solve it.
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