Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
Let an angle of a triangle is 60°. If the variance of the angles of the triangle is 4614°, then the other two angles are
MathematicsStatisticsJEE Main
Options:
  • A 23° and 97°
  • B 22° and 98°
  • C 21° and 99°
  • D 20° and 100°
Solution:
1050 Upvotes Verified Answer
The correct answer is: 21° and 99°

Let three angles of triangle be x, y & z.

As sum of three angles of triangle=180°.

x+y+z=180°

60°+y+z=180° (Given one angle is 60)

y+z=120°  1

Now, it is given that variance of the angles of triangle is equal to 4614°.

x2+y2+z23=4614°

602+y2+z23=4614°

y2+z2=10242°

y+z2-2yz=10242°

14400°-2yz=10242°  (Using 1)

yz=2079°  2

Now, y+z2=y-z2+4yz

120°=y-z2+4×2079°  (Using 1 & 2)

y-z2=14400°-8316°=6084°

y-z=78°  3

Solving equations 1 & 3, we get,

y=99° & z=21°

Thus, other two angles are 99° & 21°.

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.