Question

drag these tiles and drop them in the correct blank above
find the sum of the interior angles
substitute your x back into angle e
divide the sum by the number of sides
set up an equation with all your angles = 360

Explanation:

Step1: Recall polygon angle sum formula

For a polygon with \( n \) sides, the sum of interior angles is \( (n - 2)\times180^\circ \). A quadrilateral has \( n = 4 \), so sum is \( (4 - 2)\times180^\circ= 360^\circ \).

Step2: Identify angles in the quadrilateral

The angles are \( x + 15 \), \( 2x - 5 \), \( x + 35 \), and \( x - 5 \).

Step3: Set up the equation

Sum of angles \( = 360^\circ \), so \( (x + 15)+(2x - 5)+(x + 35)+(x - 5)= 360 \).

Step4: Simplify the left - hand side

Combine like terms: \( x+2x+x+x + 15-5 + 35-5=5x + 40 \).

Step5: Solve for \( x \)

Set \( 5x+40 = 360 \). Subtract 40 from both sides: \( 5x=360 - 40=320 \). Divide by 5: \( x=\frac{320}{5}=64 \).

Step6: Substitute \( x \) back to find each angle

• For \( x + 15 \): \( 64+15 = 79^\circ \)
• For \( 2x - 5 \): \( 2\times64-5=128 - 5 = 123^\circ \)
• For \( x + 35 \): \( 64+35 = 99^\circ \)
• For \( x - 5 \): \( 64-5 = 59^\circ \)

Answer:

The value of \( x \) is \( 64 \), and the angles are \( 79^\circ \), \( 123^\circ \), \( 99^\circ \), \( 59^\circ \) (and the equation is \( (x + 15)+(2x - 5)+(x + 35)+(x - 5)=360 \))