Melissa writes the following proof for the theorem: if the diagonals of a quadrilateral bisect each other, the quadrilateral is
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As is shown in the figure attached:
1. "A" and 76º are congruents, because they are Alternate Interior angles, so A=76º.
2. "D" and "x" are congruents, because they are Alternate Interior angles, so x=38º.
3. "A", "B" and "C" form a the triangle ABC. Then, we remember sum of the interior angles of a triangle is 180º, so we have:
76º+38º+B=180º
B=180º-76º-38º
B=66º
4. By definition, an exterior angle of a triangle is equal to the sum of the opposite interior angles to it. So, we can calculate the exterior angle "y" of the triangle ABC, as follows:
The opposite angles are: 76º and 66ª. Then, we obtain:
y=76º+66º
y=142º
Therefore, the answer is: The value of y is 142º.
1. "A" and 76º are congruents, because they are Alternate Interior angles, so A=76º.
2. "D" and "x" are congruents, because they are Alternate Interior angles, so x=38º.
3. "A", "B" and "C" form a the triangle ABC. Then, we remember sum of the interior angles of a triangle is 180º, so we have:
76º+38º+B=180º
B=180º-76º-38º
B=66º
4. By definition, an exterior angle of a triangle is equal to the sum of the opposite interior angles to it. So, we can calculate the exterior angle "y" of the triangle ABC, as follows:
The opposite angles are: 76º and 66ª. Then, we obtain:
y=76º+66º
y=142º
Therefore, the answer is: The value of y is 142º.