In given figure find the values of $x$ and $y$ , if $Q S = R Q$ .

x = 36^{\circ}, y = 32^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 45^{\circ}, y = 32^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 32^{\circ}, y = 45^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x = 45^{\circ}, y = 36^{\circ}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $x = 45^{\circ}, y = 36^{\circ}$
$G i v e n : Q S = R Q ∠ Q S P = 103, ∠ S P X = 148 ∠ S P X = ∠ Q S P + ∠ P Q S (E x t e r i o r a n g l e = S u m o t w o o p p o s i t e i n t e r i o r a n g l e s) \Rightarrow 148 = 103 + x \Rightarrow ∠ P Q S = x = 148 - 103 = 45 ∠ Q S P a m d ∠ Q S R a r e l i n e a r p a i r o f a n g l e s \Rightarrow 103 + ∠ Q S R = 180 \Rightarrow ∠ Q S R = 180 - 103 = 67 S i n c e Q S = R Q ∠ Q S R = ∠ S R Q = 67 (a n g l e s a l o n g e q u a l s i d e s a r e e q u a l) A s ∠ S R Q = ∠ P R Q I n △ R P Q 148 = ∠ P R Q + ∠ P Q R (e x t e r i o r a n g l e = s u m o f t w o o p p o s i t e i n t e r i o r a n g l e s) 148 = 67 + ∠ P Q R ∠ P Q R = 148 - 67 = 81 ∠ P Q R = ∠ S Q R + ∠ P Q S (∠ P Q R = 81 a n d ∠ P Q S = 45) \Rightarrow y = ∠ S Q R = 81 - 67 = 36 H e n c e x = 45 a n d y = 36 O p t i o n (D) i s t h e c o r r e c t a n s w e r$

Suggest Corrections

Similar questions

y = 32^{o}

z = 40^{o}

x

y + z = 90^{o}

x = 45^{o}

{(x - 2)}^{2} + {(y - 3)}^{2} = 36

{(x + 3)}^{2} + {(y + 2)}^{2} = 49

{(x - 4)}^{2} + {(y + 5)}^{2} = 64

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x-5y=20 to the circle x²+y²=9 is

M = [\begin{matrix} 3 & 2 - 1 & 4 \end{matrix}], N = [\begin{matrix} 61 \end{matrix}], X = [\begin{matrix} - 4 5 \end{matrix}], Y = [\begin{matrix} 22 \end{matrix}]

M N + 2 X - 4 Y

Join BYJU'S Learning Program