Question

what steps would you take to find the measure of angle e? recall that the sum of exterior angles is 360 divide the sum by the number of sides substitute your x back into angle e set up an equation with all your angles = the sum drag these tiles and drop them in the correct blank above

Explanation:

Step1: Recall exterior angle sum

Recall that the sum of exterior angles of any polygon is \( 360^\circ \). This is a key property for polygons.

Step2: Set up angle sum equation

Set up an equation with all the given angle expressions (in terms of \( x \)) equal to \( 360^\circ \). For example, if the angles are \( 5x + 3 \), \( 6x + 1 \), \( 8x + 8 \), \( 4x - 15 \), \( 6x + 10 \), the equation would be \( (5x + 3)+(6x + 1)+(8x + 8)+(4x - 15)+(6x + 10)=360 \).

Step3: Solve the equation for \( x \)

Combine like terms: \( (5x + 6x + 8x + 4x + 6x)+(3 + 1 + 8 - 15 + 10)=360 \) → \( 29x + 7 = 360 \). Subtract 7: \( 29x = 353 \)? Wait, maybe miscalculation. Wait, re - add: \( 5x+6x = 11x \), \( 11x + 8x=19x \), \( 19x + 4x = 23x \), \( 23x+6x = 29x \). Constants: \( 3 + 1=4 \), \( 4 + 8 = 12 \), \( 12-15=-3 \), \( -3 + 10 = 7 \). So \( 29x+7 = 360 \), \( 29x=353 \), \( x=\frac{353}{29}\approx12.17 \)? Wait, maybe the angles are for a pentagon (5 sides), so sum of interior angles is \( (5 - 2)\times180 = 540 \), but the problem says exterior angles? Wait, maybe it's interior angles. If it's interior angles of a pentagon, sum is \( 540 \). Let's recalculate: \( (5x + 3)+(6x + 1)+(8x + 8)+(4x - 15)+(6x + 10)=540 \). Combine like terms: \( 29x+7 = 540 \), \( 29x = 533 \), \( x = 18.38 \). Wait, maybe the figure is a pentagon (5 sides). Anyway, after solving for \( x \),

Step4: Substitute \( x \) into angle E

Once \( x \) is found, substitute \( x \) back into the expression for angle E (e.g., if angle E is \( 6x + 10 \), plug the value of \( x \) into this expression to find its measure.

Answer:

The steps are: 1. Recall that the sum of exterior (or interior, depending on polygon) angles is a constant (360 for exterior, (n - 2)*180 for interior, n = number of sides). 2. Set up an equation with all angle expressions equal to the total sum. 3. Solve the equation for \( x \). 4. Substitute \( x \) back into the expression for angle E to find its measure. (The first step tile is "recall that the sum of exterior angles is 360", then "set up an equation with all your angles = the sum", then solve for \( x \), then "substitute your x back into angle E".)