Sarthaks Test
+1 vote
299 views
in Mathematics by (29.7k points)

In the figure, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c

1 Answer

+1 vote
by (128k points)
selected by
 
Best answer

In the figure, lines XY and MN 

intersect at O and ∠ POY = 90°.

Also, given a : b = 2 : 3 

Let a = 2x and b = 3x. 

Since, ∠XOM + ∠POM + ∠POY = 180° 

(Linear pair axiom) 

⇒ 3x + 2x + 90° = 180° 

⇒ 5x = 180° – 90° 

⇒ x = 90 5 ° = 18° 

∴ ∠XOM = b = 3x = 3 × 18° = 54° 

and ∠POM = a = 2x = 2 × 18° = 36° 

Now, ∠XON = c = ∠MOY = ∠POM + ∠POY 

(Vertically opposite angles) 

= 36° + 90° = 126° 

Hence, c = 126° Ans.

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

...