Question

what steps would you take to find the measure of angle e? first, recall that the sum of exterior angles is 360 next. drag these tiles and drop them in the correct blank above count the number of sides set up an equation with all your angles = the sum solve for x and you’re done substitute your x back into angle e

Explanation:

Step1: Recall the sum of exterior angles

The sum of the exterior angles of any polygon is \( 360^\circ \). So we start by recalling this property.

Step2: Count the number of sides

The figure is a pentagon? Wait, no, looking at the labels (A, B, E, D, C? Wait, the figure seems to be a quadrilateral? Wait, no, the angles are labeled with expressions involving \( x \). Wait, first, count the number of angles (sides). Let's see, the angles are \( 3x - 7 \), \( x + 3 \), \( 8x - 9 \), \( 4x - 13 \), \( 2x + 10 \). Wait, that's five angles, so it's a pentagon? Wait, no, maybe a pentagon? Wait, the sum of exterior angles of any polygon is \( 360^\circ \), regardless of the number of sides (for convex polygons). Wait, first, count the number of sides (angles) to know how many terms we have. Here, there are five angles, so five terms.

Step3: Set up the equation

Sum all the angle expressions and set equal to \( 360 \). So:
\( (3x - 7) + (x + 3) + (8x - 9) + (4x - 13) + (2x + 10) = 360 \)

Step4: Solve for \( x \)

Combine like terms:
\( 3x + x + 8x + 4x + 2x - 7 + 3 - 9 - 13 + 10 = 360 \)
\( (3 + 1 + 8 + 4 + 2)x + (-7 + 3 - 9 - 13 + 10) = 360 \)
\( 18x + (-16) = 360 \)
\( 18x = 360 + 16 \)
\( 18x = 376 \)? Wait, no, let's recalculate the constants:
\( -7 + 3 = -4 \); \( -4 - 9 = -13 \); \( -13 - 13 = -26 \); \( -26 + 10 = -16 \). So \( 18x - 16 = 360 \)
\( 18x = 360 + 16 = 376 \)? Wait, that can't be, maybe I miscounted the number of angles. Wait, maybe it's a quadrilateral? Wait, the figure: let's check the labels. The vertices are A, B, E, D, C? Wait, maybe it's a pentagon, but maybe I made a mistake. Wait, let's re-express the angles:
\( 3x - 7 \), \( x + 3 \), \( 8x - 9 \), \( 4x - 13 \), \( 2x + 10 \). Let's add them:
\( 3x + x + 8x + 4x + 2x = 18x \)
\( -7 + 3 = -4 \); \( -4 - 9 = -13 \); \( -13 - 13 = -26 \); \( -26 + 10 = -16 \). So \( 18x - 16 = 360 \)
\( 18x = 376 \) → \( x = 376 / 18 = 188 / 9 ≈ 20.89 \). But maybe I miscounted the number of angles. Wait, maybe it's a quadrilateral (four angles). Let's check the figure again. If it's a quadrilateral, then four angles. Let's see: maybe the angles are \( 3x - 7 \), \( x + 3 \), \( 8x - 9 \), \( 4x - 13 \), and \( 2x + 10 \) is a mistake? Wait, no, the problem says "set up an equation with all your angles = the sum". Wait, maybe the figure is a pentagon, so five angles. Anyway, proceed with the equation.

Step5: Substitute \( x \) back into angle E

Angle E is \( 2x + 10 \). Once we have \( x \), substitute to find its measure.

Wait, maybe I made a mistake in the number of sides. Let's check the sum of exterior angles: for any convex polygon, the sum of exterior angles is \( 360^\circ \), regardless of the number of sides (n ≥ 3). So whether it's a triangle (3 sides), quadrilateral (4), pentagon (5), etc., the sum is \( 360^\circ \). So the steps are:

1. Recall the sum of exterior angles is \( 360^\circ \).
2. Count the number of angles (sides) to know how many terms to sum.
3. Set up the equation by summing all angle expressions and setting equal to \( 360 \).
4. Solve for \( x \).
5. Substitute \( x \) back into the expression for angle E to find its measure.

So the correct order of steps (from the tiles) is:

First: recall that the sum of exterior angles is 360.

Next: count the number of sides (angles).

Then: set up an equation with all your angles = the sum (360).

Then: solve for \( x \).

Then: substitute your \( x \) back into angle E.

So the drag-and-drop order would be:

1. recall that the sum of exterior angles is 360

2. count the number of sides

3. set up an equation with all your angles = the sum

4. solve for x and you're done

5. substitute your x back into angle E

Answer:

The correct order of steps (from the given tiles) is:

1. recall that the sum of exterior angles is 360
2. count the number of sides
3. set up an equation with all your angles = the sum
4. solve for x and you're done
5. substitute your x back into angle E

(Note: The actual calculation of \( x \) and the measure of angle E would follow after setting up the equation, but the question is about the steps to take, not the numerical answer.)