Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

In the parallelogram LOST shown below, $S N ⊥ O L$ and $S M ⊥ L T$ and . Find $∠ S T M, ∠ S O N$ . Find and $∠ N S M$ and , and choose the option which represents the same.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

50 °, 50 °, 50 °

60 °, 50 °, 70 °

60 °, 55 °, 75 °

50 °, 55 °, 65 °

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Here, we are given a parallelogram LOST with

S N ⊥ O L

and

S M ⊥ L T

.
We have, to calculate the angle measures of

∠ S T M, ∠ S O N

and

∠ N S M

.
Now, we know that the angle sum property of a triangle says that sum of all the interior angles of a triangle is always

180 ∘

.
Using this property in

△ M S T

, we get,

∠ T M S + ∠ M S T + ∠ S T M = 180 ° ∠ S T M = 180 ° − (90 ° + 40 °) ∠ S T M = 50 °

Next, it is the property of a parallelogram that its opposite angle pairs are equal.
So, using this property, we have,

∠ S O N = ∠ S T M = 50 ∘

Now, again using the angle sum property of a triangle in

△ S O N

, we get,

∠ O N S + ∠ O S N + ∠ S O N = 180 ° ∠ O S N = 180 ° − (90 ° + 50 °) ∠ O S N = 40 °

Again, it is the property of a parallelogram that the adjacent angle pairs are supplementary, i.e., they add up to

180 ∘

.
Applying this property on the parallelogram LOST, we get,

∠ S O N + ∠ T S O = 180 ° ∠ S O N + ∠ T S M + ∠ N S M + ∠ O S N = 180 ° 50 ° + 40 ° + ∠ N S M + 40 ° = 180 ° 130 ° + ∠ N S M = 180 ° ∠ N S M = 180 ° − 130 ° ∠ N S M = 50 °

So, the angle measures are found as,

∠ S T M = 50 °, ∠ S O N = 50 °

and

∠ N S M = 50 °

.
Hence, the correct option is (1).

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!