Question

PQ and QR are two sides of a regular 12 sided polygon. PR is diagonal of the polygon. Work out the size of angle PQR

Answer 1

Answer:

The size of angle PQR is 150°

Step-by-step explanation:

Lets explain how to solve the problem

- A polygon is regular when all its angles are equal and all its sides

  are equal

- The measure of each interior angle an any regular polygon

   = $\frac{(n-2)*180}{n}$, where n is the number of its angles or its sides

∵ PQ and QR are two sides of a regular 12 sided polygon

∴ Q is one of its vertex

- We need to find the size of angle PQR

∵ Angle PQR is an interior angle in the regular 12 sided polygon

∴ n = 12

Use the rule above to find the size of the angle PQR

∵ The size of ∠PQR = $\frac{(12-2)*180}{12}$

∴ The size of ∠PQR = $\frac{(10)*180}{12}$

∴ The size of ∠PQR = $\frac{1800}{12}=150$

∴ The size of angle PQR = 150°

* The size of angle PQR is 150°

Answer 2

PQ and QR are two sides of a regular 12 sided polygon. PR is diagonal of the polygon then the size of angle PQR is $150^\circ$ and this can be determined by using the formula of a number of sides of the polygon.

Given :

• PQ and QR are two sides of a regular 12 sided polygon.
• PR is diagonal of the polygon.

The formula for the sides of the polygon is given by:

$\rm S = \dfrac{(n-2)\times 180}{n}$

where 'S' is the measure of each interior angle in any regular polygon and 'n' is the number of sides.

Now put the value of 'n' in equation (1) to get the measure of angle PQR.

$\rm \angle PQR = \dfrac{(12-2)\times 180}{12}$

$\rm \angle PQR = \dfrac{10\times 180}{12}$

$\rm \angle PQR = 150^\circ$

PQ and QR are two sides of a regular 12 sided polygon. PR is diagonal of the polygon then the size of angle PQR is $150^\circ$.

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https://brainly.com/question/24006293