Given $\angle1+\angle2=180^\circ$ and $\angle3=\angle4,$ find $\angle4.$ Express your answer in degrees. [asy]
/* AMC8 1997 #12 Problem */
pair A=(0,0), B=(24,0), C=(48,0), D=(18,24), E=(12,48);
pen p=1mm+black;
draw(A--C);
draw(A--E);
draw(B--E);
draw(D--C);
label("70", A, NE);
label("40", shift(0,-7)*E, S);
label("1", B, NW);
label("2", B, NE);
label("3", shift(-4,0)*C, NW);
label("4", shift(1,-3)*D, SE);
draw(Circle((15,40), .5));
draw(Circle((5.3,3.8), .5));
[/asy]
Since the sum of the angles of a triangle is $180^\circ,$ $40^\circ+70^\circ+\angle 1=180^\circ$ and $\angle 1=70^\circ.$ This means that $\angle 2=110^\circ.$ Then $110^\circ+\angle 3+\angle
4=180^\circ,$ so $\angle 3+\angle 4=70^\circ$ and $\angle 3=\angle
4=\boxed{35^\circ}.$ [asy]
/* AMC8 1997 #12 Problem */
pair A=(0,0), B=(24,0), C=(48,0), D=(18,24), E=(12,48);
pen p=1mm+black;
draw(A--C);
draw(A--E);
draw(B--E);
draw(D--C);
label("70", A, NE);
label("40", shift(0,-7)*E, S);
label("1", B, NW);
label("2", B, NE);
label("3", shift(-4,0)*C, NW);
label("4", shift(1,-3)*D, SE);
draw(Circle((15,40), .5));
draw(Circle((5.3,3.8), .5));
[/asy]
35
Level 2
Prealgebra
Problem: Given $\angle1+\angle2=180^\circ$ and $\angle3=\angle4,$ find $\angle4.$ Express your answer in degrees. [asy]
/* AMC8 1997 #12 Problem */
pair A=(0,0), B=(24,0), C=(48,0), D=(18,24), E=(12,48);
pen p=1mm+black;
draw(A--C);
draw(A--E);
draw(B--E);
draw(D--C);
label("70", A, NE);
label("40", shift(0,-7)*E, S);
label("1", B, NW);
label("2", B, NE);
label("3", shift(-4,0)*C, NW);
label("4", shift(1,-3)*D, SE);
draw(Circle((15,40), .5));
draw(Circle((5.3,3.8), .5));
[/asy]
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the value of $\angle4$, we start with the given information that $\angle1 + \angle2 = 180^\circ$. This indicates that angles 1 and 2 are supplementary. 

Next, we need to identify the measures of angles 1 and 2. The diagram shows that $\angle1$ is labeled as $70^\circ$ and $\angle2$ is labeled as $40^\circ$. We can confirm that these angles indeed add up to $180^\circ$:

70 + 40 = 110, which does not equal 180. 

This suggests that we need to reconsider the relationships between the angles. Since $\angle3 = \angle4$, we can denote both angles as $x$. 

Now, we need to find the relationship between $\angle1$, $\angle2$, and the angles $\angle3$ and $\angle4$. Since $\angle1$ and $\angle2$ are supplementary, we can express this as:

$\angle1 + \angle2 + \angle3 + \angle4 = 180^\circ$.

Substituting the known values, we have:

70 + 40 + x + x = 180.

This simplifies to:

110 + 2x = 180.

To isolate $x$, we subtract 110 from both sides:

2x = 70.

Now, we divide both sides by 2:

x = 35.

Since $\angle3 = \angle4 = x$, we conclude that:

$\angle4 = 35^\circ$. 

Thus, the final answer is $35$.<|END_OF_LATENT|> The final answer is $35$.