+1712 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:
\(∠b=100 \\∠e=140 \\∠c=40 \\∠a=40 \\sum=100+140+40+40 \\sum=240+40+40 \\sum=240+80 \\sum=320\)
