In a regular pentagon PQRST , PR intersects QS at O. Calculate ROS?


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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

$P Q = Q R ∴ ∠ P R Q = \frac{180 - 108}{2} = 36$ $∠ O R S = 108 - 36 = 72 °$ $Q R = R S ∠ O S R = 36 °$ $∠ R O S = 180 - 72 - 36 = 72 °$
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