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

If a quadrilateral has three acute angles, each measuring 75°, then the measure of the fourth angle is ____°.

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

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

If a quadrilateral has three acute angles, each measuring 75°, then the measure of the fourth angle is 135°.
Given, measure of three angles of a quadrilateral as

75 °

.
Let the three angles i.e,

∠ A, ∠ B, ∠ C

be given as

75 °

.
Consider the value of fourth angle of quadrilateral

A B C D, ∠ D = x

⇒ ∠ A = 75 °, ∠ B = 75 °, ∠ C = 75 °, ∠ D = x

Then, sum of interior angles of a quadrilateral is equal to

360 °

.
In quadrilateral ABCD,

⇒ ∠ A + ∠ B + ∠ C + ∠ D = 360 °

Substituting the values of angles,

⇒ 75 ° + 75 ° + 75 ° + x = 360 °

⇒ 225 ° + x = 360 °

⇒ x = 360 ° − 225 °

⇒ x = 135 °

∴ ∠ D = 135 °

Hence, the value of fourth angle of the quadrilateral is

135 °

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!