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Find the sum of angles a, b, c, e. Dec 1, 2019

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Work:

Let us start by finding ∠b.

Because the uppermost triangle with no a, e or c is isosceles, the angles opposite the congruent sides are congruent.

This means that the formula to find ∠b is this:

$$∠b=180-40-40$$

This is because the sum of the interior angles of the triangle is 180, and in order to find b, we had to "eliminate" the 40-degree angles.

Simplifying, we get:

$$∠b=140-40 \\∠b=100$$

After we decided the answer to ∠b, let us move onto the measure of ∠e.

Since we have already concluded that the angle "on top" (for lack of a better term) of ∠e is 40, we can use supplementary angles to figure it out.

In this case, the equation would be:

$$∠e=180-40 \\∠e=140$$

After we have decided the answer to ∠e, let us move onto the measure of∠c.

Using corresponding angles with the fact that the lines are parallel, the measure of angle c is congruent to the measure of the angle on top of angle e, which shows that:

$$∠c=40$$

After we have deduced the answer to ∠c, let us move onto the measure of ∠a.

Using corresponding angles with the fact that the lines are parallel, the measure of angle a is congruent to the measure of the angle opposite the angle on top of angle e, which shows that:

$$∠a=40$$

Now, let us add it all up:

$$∠b=100 \\∠e=140 \\∠c=40 \\∠a=40 \\sum=100+140+40+40 \\sum=240+40+40 \\sum=240+80 \\sum=320$$

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Dec 1, 2019