CAT 2019 Shift 2 Paper

Question : 73 of 100

Marks: +1, -0

Let A and B be two regular polygons having a and b sides, respectively. If b = 2aand each interior angle of B is 3/2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is

Your Answer:

Validate

Solution:

The formula for each interior angle

=180-\;{360}/{n},

where 'n' is the side of the regular polygon

⇒ 180-\;{360}/{2 a}=\;{3}/{2}(180-\;{360}/{a})

⇒ 360-\;{360}/{a}=540-\;{3 × 360}/{a}

⇒ \;{2 × 360}/{a}=180

⇒ a=\;{2 × 360}/{180}

⇒ a=4 \;\text " and "\; b=2 a=8

Polygon with each side

=a+b=4+8=12,

will have each interior angle

=180-\;{360}/{12}

=150

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