Find the value of y for which line a is parallel to line b

Mathematics

1 answer:

Vsevolod [243]4 years ago

3 0

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.

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