Advertisements
Advertisements
Question
Two lines AB and CD intersect at O. If `∠`AOC + `∠`COB + `∠`BOD = 270°, find the
measures of `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA.
Advertisements
Solution
Given: `∠`AOC + `∠`COB + `∠`BOP = 270°
To find: `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA
Here, `∠`AOC + `∠`COB + `∠`BOD + `∠`AOD = 360° [Complete angle]
⇒ 270 + `∠`AOD = 360°
⇒ `∠` AOD = 360° - 270°
⇒ `∠`AOD = 90°
Now,
`∠`AOD + `∠`BOD = 180° [Linear pair]
90 + `∠`BOD = 180°
⇒ `∠`BOD = 180° - 90°
∴ `∠`BOD = 90°
`∠`AOD = `∠`BOC = 90° [Vertically opposite angles]
`∠`BOD = `∠`AOC = 90° [Vertically opposite angles]
APPEARS IN
RELATED QUESTIONS
If one of the four angles formed by two intersecting lines is a right angle, then show that
each of the four angles is a right angle.
In the below fig, rays AB and CD intersect at O.
Determine y when x = 60°
In the below fig, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠COF,
∠DOE and ∠BOF.
In the given figure, AOB is a straight line. If ∠AOC + ∠BOD = 85°, then ∠COD =
In the given figure, the value of y is
Give two examples of perpendicular lines you can see in your environment.
Look at the picture given below. Decide whether the lines given in picture is parallel or perpendicular to each other and write the answer in the box.
Look at the picture given below. Decide whether the lines given in picture is parallel or perpendicular to each other and write the answer in the box.
What is the geometric relationship between two straight lines in the same plane that will never intersect, no matter how much they are extended?
In the example of a 'Zebra crossing,' what feature specifically exemplifies the constant distance property of parallel lines?
