Geometry and Angles in Polygons Practice Problems

Vocabulary flashcards providing step-by-step angle and polygon calculations for practice problems on the worksheet.

Question 2a: Value of $\theta$

$57^\circ$ (calculated using parallel line angle rules: $131^\circ - 56^\circ - 18^\circ = 57^\circ$)

Question 2b: Value of $\theta$ in the regular pentagon

$36^\circ$ (calculated by dividing the interior angle of a regular pentagon, $108^\circ$, into 3 equal parts)

Question 3: Sum of interior angles of a 15-sided regular shape

$2340^\circ$ (calculated using $(n - 2) \times 180^\circ = (15 - 2) \times 180^\circ = 13 \times 180^\circ = 2340^\circ$)

Question 4: Number of sides of a regular shape with exterior angle $24^\circ$

$15$ sides (calculated using $\frac{360^\circ}{24^\circ} = 15$)

Question 5: Number of sides of a regular shape with interior angle $150^\circ$

$12$ sides (calculated using exterior angle $180^\circ - 150^\circ = 30^\circ$ and $\frac{360^\circ}{30^\circ} = 12$)

Question 6: Polygon with interior and exterior angles in the ratio $7 : 2$

Nonagon (a 9-sided regular polygon, calculated using exterior angle $\frac{2}{9} \times 180^\circ = 40^\circ$ and $\frac{360^\circ}{40^\circ} = 9$)

Question 7: Size of angle $B$ in a pentagon with given angles $80^\circ$, $130^\circ$, $120^\circ$ and angle ratio $A : B = 3 : 4$

$120^\circ$ (calculated using total interior angle sum $540^\circ$; $A + B = 540^\circ - 330^\circ = 210^\circ$; angle $B = \frac{4}{7} \times 210^\circ = 120^\circ$)

Question 8: Value of $\theta$ between parallel lines

$119^\circ$ (calculated using co-interior angles: $(180^\circ - 140^\circ) + (180^\circ - 101^\circ) = 40^\circ + 79^\circ = 119^\circ$)

Question 9: Value of $\theta$ between parallel lines

$86^\circ$ (calculated using interior angle $360^\circ - 232^\circ = 128^\circ$, alternate angle $34^\circ$, and co-interior angle $180^\circ - (128^\circ - 34^\circ) = 86^\circ$)

Sum of Interior Angles Formula

$(n - 2) \times 180^\circ$, where $n$ is the number of sides of the polygon

Exterior Angle Formula for Regular Polygons

$\frac{360^\circ}{n}$, where $n$ is the number of sides of the regular polygon