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Find the sum of angles a, b, c, e.

 

 Dec 1, 2019
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Answer: 320

 

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

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