E-Math – Geometry – Find the angles between two adjacent polygons Source: Math Tutor 4b, Casco, 2010, Quick Review 6, q21b

In the diagram, ABCDEFG...is part of a regular polygon with n sides. Each interior angle of this polygon is 150o. BPQRSTUC is a regular octagon. Find

i) the value of n,

Formula: (𝑛−2)×180𝑜

𝑛 Each angle of a Regular

Polygon, where n is the number of sides.

(𝑛−2)×180𝑜

𝑛= 150𝑜

(𝑛 − 2) × 180𝑜 = 150𝑛𝑜

180𝑛𝑜 − 360𝑜 = 150𝑛𝑜

180𝑛𝑜 − 150𝑛𝑜 = 360𝑜

30𝑛𝑜 = 360𝑜

𝑛 =36030

= 12 𝑠𝑖𝑑𝑒𝑠

ii) ∠ABP,

www.tuitionwithjason.sg

iii) ∠APB,

iv) ∠BCF,

v)∠CDF