Question

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

Answer 1

The size of angle PRQ is 15°

Step-by-step explanation:

In any regular polygon of n-sided

• All sides are equal in length
• All angles are equal in measure
• The measure of each interior angle is $\frac{(n-2)*180}{n}$
• The measure of each exterior angle is $\frac{360}{n}$
• The sum of the measures of the interior and exterior angle at the same vertex is 180°

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

∴ PQ = QR

∵ PR is a diagonal

∴ ∠PQR is an interior angle of the polygon

- By using the rule of the interior angle above

∵ n = 12

∴ m∠PQR = $\frac{(12-2)*180}{12}$

∴ m∠PQR = 150°

In Δ PQR

∵ PQ = QR ⇒ sides in a regular polygon

- Δ PQR is an isosceles Δ

∴ m∠PRQ = m∠RPQ ⇒ base angles of an isosceles Δ

The sum of the measures of the interior angles of a triangle is 180°

∵ m∠PQR + m∠PRQ + m∠RPQ = 180°

∴ 150 + m∠PRQ + m∠RPQ = 180°

- Subtract 150 from both sides

∴ m∠PRQ + m∠RPQ = 30

∵ m∠PRQ = m∠RPQ

- Divide their sum by 2 to find the measure of each one

∴ m∠PRQ = m∠RPQ = 30 ÷ 2 = 15°

∴ m∠PRQ = 15°

The size of angle PRQ is 15°

Learn more:

You can learn more about the triangles in brainly.com/question/3945600

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