Question

Hello, this is for test revision, my test is tomorrow.

I've already got the answer, I just need a valid explanation and method, please, using the following formula :

Single interior angle in a regular polygon :
( n - 2 ) x 180 / n

( n represents the number of sides ) .

Thank you.

Answer 1

y = 44°

Explanation:

The sum of angles around a point is always 360°.

To determine the measure of angle y, simply subtract the measure of the interior angle of Shape A and the measure of the interior angle of Shape B from 360°.

The formula to find the measure of the interior angle a regular polygon with "n" sides is:

`\textsf{Interior angle of a regular polygon} = (180^(\circ)(n-2))/(n)`

Given Shape A is a regular polygon with 15 sides, the measure of its interior angle is:

`\begin{aligned}\textsf{Interior angle of Shape A} &= (180^(\circ)(15-2))/(15)\\\\&= (180^(\circ)(13))/(15)\\\\&= (2340^(\circ))/(15)\\\\&=156^(\circ)\end{aligned}`

Given Shape B is a regular polygon with 18 sides, the measure of its interior angle is:

`\begin{aligned}\textsf{Interior angle of Shape B} &= (180^(\circ)(18-2))/(18)\\\\&= (180^(\circ)(16))/(18)\\\\&= (2880^(\circ))/(18)\\\\&=160^(\circ)\end{aligned}`

Subtract the interior angles of Shape A and Shape B from 360°:

`\begin{aligned}y &=360^(\circ)-156^(\circ)-160^(\circ)\\\\y &=204^(\circ)-160^(\circ)\\\\y &=44^(\circ)\end{aligned}`

Therefore, the size of angle y is 44°.