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Vikki [24]
2 years ago
6

PQ and QR are 2 sides of a regular 10-sided polygon

Mathematics
2 answers:
gladu [14]2 years ago
8 0

Answer:

Step-by-step explanation:

Measure of inner angle of the n-sided polygon is

\frac{180(n-2)}{n}

~~~~~~~~~~~~~~

m∠PQR = \frac{180(10-2)}{10} = 144°

PQ = QR ⇒ m∠QPR = m∠QRP

<em>m∠PRQ =</em> ( 180° - 144° ) ÷ 2 = <em>18 </em>°

AVprozaik [17]2 years ago
8 0

Answer:

∠PRQ = 18°

Step-by-step explanation:

<u />

Sum of interior angles of a polygon = (n - 2) × 180°
(where n is the number of sides)

Interior angle of a regular polygon = sum of interior angles ÷ n
(where n is the number of sides)

Given:

  • n = 10

⇒ Sum of interior angles of a polygon = (10 - 2) × 180° = 1440°

⇒ Interior angle of a regular polygon = 1440° ÷ 10 = 144°

Therefore, as PQ and QR are the sides of the polygon, ∠PQR = 144°

Sum of interior angles of a triangle = 180°

⇒ ∠PQR + ∠RPQ + ∠PRQ = 180°

⇒ 144° + ∠RPQ + ∠PRQ = 180°

⇒ ∠RPQ + ∠PRQ = 36°

As the polygon is regular, PQ = QR which means that ΔPQR is isosceles.

Therefore, ∠RPQ = ∠PRQ

⇒ ∠PRQ = 36° ÷ 2 = 18°

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