In Figure, if AB\(||\)CD, EF\(⊥\)CD and \(∠ \)GED=126°, find \(∠ \)AGE,\(∠ \)GEF and \(∠ \)FGE.
Solution and Explanation
It is given that, AB \(||\) CD.
EF \(⊥\) CD
\(∠\)GED = 126º
\(⇒\) ∠GEF + \(∠\)FED = 126º
\(⇒\) \(∠\)GEF + 90º = 126º
\(⇒\) \(∠\)GEF = 36º
\(∠\)AGE and \(∠\)GED are alternate interior angles.
\(⇒\) \(∠\)AGE = \(∠\)GED = 126º
However, \(∠\)AGE + \(∠\)FGE = 180º (Linear pair)
\(⇒\) 126º + \(∠\)FGE = 180º
\(⇒\)\(∠\)FGE = 180º − 126º = 54º
∴ \(∠\)AGE = 126º, \(∠\)GEF = 36º, \(∠\)FGE = 54º
Top Questions on Lines Parallel to the Same Line
- In Figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB \(||\) CD.
- CBSE Class IX
- Mathematics
- Lines Parallel to the Same Line
- In Figure, if AB \(||\) CD, \(∠\) APQ = 50° and \(∠\) PRD = 127°, find x and y.
- CBSE Class IX
- Mathematics
- Lines Parallel to the Same Line
- In Figure, if PQ\(||\)ST, \(∠\)PQR=110° and \(∠\)RST=130°, find \(∠\)QRS. [Hint: Draw a line parallel to ST through point R.]
- CBSE Class IX
- Mathematics
- Lines Parallel to the Same Line
- In the given figure, if AB \(||\) CD, CD \(||\) EF and y: z = 3: 7, find x.
- CBSE Class IX
- Mathematics
- Lines Parallel to the Same Line
Questions Asked in CBSE Class IX exam
- What are the main features of the mechanical teachers and the schoolrooms that Margie and Tommy have in the story?
- CBSE Class IX
- The fun they had
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play
- CBSE Class IX
- The fun they had
- Is there any difference between the two roads as the poet describes them:
(i) in stanzas two and three?
(ii) in the last two lines of the poem?- CBSE Class IX
- The fun they had
- Here is your diary entry when you visited Agra. Read the points and try to write a travelogue describing your visit to Agra and the Taj Mahal. You may add more details.
January 2003 — rise before dawn — take the Shatabdi Express at 6.15 a.m. from Delhi — meet a newly-married couple on train — talk about Himachal Pradesh — get off the train — enter the once-grand city, Agra — twisted alleys — traffic dense — rickshaws, cars, people — vendors selling religious artifacts, plastic toys, spices and sweets — go to the Taj Mahal — constructed entirely of white marble — magical quality — colour changes with varying of light and shadow — marble with gemstones inside — reflection of the Taj Mahal in the pond — school-children, tourists — tourist guides following people.- CBSE Class IX
- Kathmandu
- 1.The (site, cite) of the accident was (ghastly/ghostly).
2. Our college (principle/principal) is very strict.
3. I studied (continuously/continually) for eight hours.
4. The fog had an adverse (affect/effect) on the traffic.
5. Cezanne, the famous French painter, was a brilliant (artist/artiste).
6. The book that you gave me yesterday is an extraordinary (collage/college) of science fiction and mystery. 7. Our school will (host/hoist) an exhibition on cruelty to animals and wildlife conservation.
8. Screw the lid tightly onto the top of the bottle and (shake/shape) well before using the contents.- CBSE Class IX
- If I were you