Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
621 views
in Lines and Angles by (38.0k points)
closed by

Prove that the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

1 Answer

+1 vote
by (36.4k points)
selected by
 
Best answer

Consider the angles,

∠AOB and ∠ACB

Given that,

OA perpendicular AO and OB perpendicular BO

To prove:

∠AOB = ∠ACB or,

∠AOB + ∠ACB = 180°

Proof: In a quadrilateral

∠A + ∠O + ∠B + ∠C = 360°(Sum of angles of a quadrilateral)

180° + ∠O + ∠C = 360°

∠O + ∠C = 180°

Hence,

∠AOB + ∠AOC = 180°(i)

Also,

∠B +∠ACB = 180°

∠ACB = 180° – 90°

∠ACB = 90°(ii)

From (i) and (ii), we get

∠ACB = ∠AOB = 90°

Hence, the angles are equal as well as supplementary

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...