Exercise 83 Page 513

Practice makes perfect

An interior angle and corresponding exterior angle of a polygon form a linear pair, which means they are supplementary angles.

If we call the interior angle of the polygon θ, we can write and solve the following equation to find its measure. 29^(∘)+m∠ θ =180^(∘) ⇔ m∠θ=151^(∘)

In a regular polygon with n sides, the measure of all interior angles is the same. Therefore, if one interior angle is 170^(∘), the sum of all of its angles must be 170^(∘) n.

Also, the sum of the measures of the interior angles in an n-gon is 180^(∘)(n-2). With this information, we can write the following equation. 180^(∘)(n-2)=170^(∘) n If this is a regular polygon, we should get an integer when solving for n.

180^(∘)(n-2)=170^(∘) n

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Solve for n

Distr

Distribute 180^(∘)

180^(∘) n-360=170^(∘) n

SubEqn

LHS-170^(∘) n=RHS-170^(∘) n

10^(∘) n-360^(∘)=0

AddEqn

LHS+360^(∘)=RHS+360^(∘)

10^(∘) n=360^(∘)