AI Mentor

Check Your IQ

Free Expert Demo

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

The 2 nonadjacent sides of a regular pentagon (5 congruent and 5 congruent interior angles) are extended to meet at point X as shown in the above figure. Find the measure of ∠X.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

°

°

°

°

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The sum of interior angles of the pentagon is

(n - 2) \times 180 °

At n=5,

(5 - 2) \times 180 ° = 540

Since, it is a regular pentagon, the value of each of the interior angle is=

\frac{540 °}{5}

= 180

°

The two-base angle of the triangle forms a linear pair with the interior angles of the pentagon. Hence the measure of the two base angle of the triangle is 180

°

−108

°

= 72

°

.
Hence x=180

°

− (720+720) = 180

°

−144

°

= 36

°

.
Hence option (3) is the correct answer.

Watch 3-min video & get full concept clarity

courses

No courses found

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!