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=40sum=100+140+40+40sum=240+40+40sum=240+80sum=320
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