In-a-regular-pentagon-PQRST-PR-intersects-QS-at-O-Calculate-ROS-

Question Number 204541 by necx122 last updated on 21/Feb/24

I n a r e g u l a r p e n t a g o n P Q R S T, P R

i n t e r s e c t s Q S a t O . C a l c u l a t e R O S ?

Commented by som(math1967) last updated on 21/Feb/24

∡ R O S = 72 °

Commented by necx122 last updated on 21/Feb/24

p l e a s e e x p l a i n w i t h d i a g r a m s i r .

T h a n k y o u i m m e n s e l y .

Commented by som(math1967) last updated on 21/Feb/24

Commented by som(math1967) last updated on 21/Feb/24

P Q = Q R ∴ ∠ P R Q = \frac{180 - 108}{2} = 36

∠ O R S = 108 - 36 = 72 °

Q R = R S ∠ O S R = 36 °

∠ R O S = 180 - 72 - 36 = 72 °