Question

PQ, QR and RS are the consecutive sides of a regular polygon. If angle

QPR = 180

, find the number of sides.​

Answer 1

Answer:

HOPE IT HELPS YOU!!!

Step-by-step explanation:

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  

The measure of each exterior angle is  

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 =  

∴ 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