Question

1 interior angle measure: 1 exterior angle measure: 2. sum of interior angles: 1 interior angle measure: 1 exterior angle measure: 3. imagine a regular polygon with 12 sides. sum of interior angles: 1 interior angle measure: 1 exterior angle measure: 4. find x in the triangle. 15 + x 47° 18 + 4x

Explanation:

Step1: Determine n for Q2 (octagon, n=8)

Sum of interior angles: $(8-2)\times180^\circ=1080^\circ$

Step2: 1 interior angle (Q2)

$\frac{1080^\circ}{8}=135^\circ$

Step3: 1 exterior angle (Q2)

$\frac{360^\circ}{8}=45^\circ$

Step4: Sum for Q3 (n=12)

$(12-2)\times180^\circ=1800^\circ$

Step5: 1 interior angle (Q3)

$\frac{1800^\circ}{12}=150^\circ$

Step6: 1 exterior angle (Q3)

$\frac{360^\circ}{12}=30^\circ$

Step7: Triangle angle sum (Q4)

$47+(15+x)+(18+4x)=180$

Step8: Solve for x (Q4)

$80+5x=180\Rightarrow x=20$

Answer:

Sum of Interior Angles (Q2): $1080^\circ$, 1 Interior Angle Measure (Q2): $135^\circ$, 1 Exterior Angle Measure (Q2): $45^\circ$
Sum of Interior Angles (Q3): $1800^\circ$, 1 Interior Angle Measure (Q3): $150^\circ$, 1 Exterior Angle Measure (Q3): $30^\circ$
x (Q4): $20$