3 -bob planimetriya 1 Burchaklar. Masofalar

3 -Bob PLANIMETRIYA

3.1 Burchaklar. Masofalar

1. Qo'shni burchaklar yig'indisi 180 ⁰ ga teng

2. Vertikal burchaklar teng.

(96-3-37) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan

qo'shni burchaklarning gradus o'lchovlari 2 : 3 nisbat-

da bo'lsa, shu burchaklarni toping.

A) 72⁰; 108⁰ B) 60⁰; 120⁰ C) 30⁰; 150⁰ D) 50⁰; 130⁰

E) 62⁰; 118⁰ Yechish: Masalaning shartida keltirilgan

qo'shni burchaklar α va β bo'lsin. U holda

tenglamalar sistemasini hosil qilamiz. Birinchi tenglama-

dan α ni topamiz.

Uni ikkinchi tenglamaga qo'yamiz va hosil bo'lgan teng-

lamani yechamiz.

⁰

α=180⁰-β=72⁰ bo’ladi. J:72⁰;108⁰(A)

1. (96-3-36) Qo'shni burchaklardan biri ikkinchisidan 16⁰ katta. Shu qo'shni burchaklarni toping.

A) 16⁰; 164⁰ B) 80⁰; 96⁰ C) 148⁰; 32⁰ D) 82⁰; 98⁰ E) 62⁰; 118⁰

2. (96-1-37) Ikkita to'g'ri chiziqning kesishishidan hosil bo'lgan uchta burchakning yig'indisi 315⁰

ga teng. Shu burchaklardan kichigini toping.

A) 60⁰ B) 45⁰ C) 10⁰ D) 85⁰ E) 50⁰

3. (96-10-40) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan burchaklarning ayirmasi 40⁰ ga teng. Kichik

burchakni toping.

A) 60⁰ B) 40⁰ C) 50⁰ D) 70⁰ E) 45⁰

4. (96-9-88) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan uchta burchak yig'indisi 265⁰ ga teng.

Shu burchaklardan kattasini toping.

A) 110⁰ B) 95⁰ C) 105⁰ D) 150⁰ E) 120⁰

5. (96-11-37) Qo'shni burchaklardan biri ikkinchisidan20⁰ ga katta. Shu qo'shni burchaklarni toping.

A) 160⁰; 20⁰ B) 28⁰; 152⁰ C) 20⁰; 160⁰ D) 140⁰; 40⁰ E) 80⁰; 100⁰

6. (96-11-38) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan qo'shni burchaklar 5 : 7 nisbatda bo'lsa,

shu burchaklarni toping.

A) 36⁰; 144⁰ B) 75⁰; 105⁰ C) 42⁰; 138⁰ D) 38⁰; 142⁰ E) 85⁰; 95⁰

7. (96-12-38) Qo'shni burchaklardan biri ikkinchisidan

18⁰ katta. Shu qo'shni burchaklarni toping.

A) 82⁰; 98⁰ B) 81⁰; 99⁰ C) 80⁰; 100⁰ D)162⁰; 18⁰ E) 98⁰; 82⁰

8. (96-12-39) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan qo'shni burchaklarning gradus o'lchovlari

3 : 7 nisbatda bo'lsa, shu burchaklarni toping.

A) 60⁰; 120⁰ B) 30⁰; 150⁰ C) 54⁰; 126⁰ D) 62⁰; 118⁰ E) 40⁰; 140⁰

9. (97-1-27) Ikki qo'shni burchakning ayirmasi 24⁰ ga teng. Shu burchaklardan kichigini toping.

A) 72⁰ B) 68⁰ C) 82⁰ D) 76⁰ E) 78⁰

10. (97-4-43) Qo'shni burchaklardan biri ikkinchisidan4 marta kichik bo'lsa, shu burchaklardan kattasi-

ni toping.

A) 125⁰ B) 130⁰ C) 140⁰ D) 144⁰ E) 120⁰

11. (97-5-3) Soatning minut mili 9 minutda necha gradusga buriladi?

A) 15⁰ B) 30⁰ C) 25⁰ D) 54⁰ E) 60⁰

12. (97-5-41) Burchakning bissektrisasi uning tomoni bilan 15⁰ li burchak tashkil etsa, burchakning

o'zini toping.

A) 45⁰ B) 30⁰ C) 60⁰ D) 90⁰ E) 7, 5⁰

13. (97-6-27) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan burchaklarning kattaliklari nisbati 7 : 3

ga teng. Shu burchaklardan kichigini toping.

A) 63⁰ B) 51⁰ C) 57⁰ D) 48⁰ E) 54⁰

14. (97-9-3) Soatning minut mili 6 minutda necha gradusga buriladi?

A) 20⁰ B) 24⁰ C) 36⁰ D) 40⁰ E) 60⁰

15. (97-9-41) Burchakning bissektrisasi uning tomoni bilan 45⁰ li burchak tashkil etsa, burchakning

o'zini toping.

A) 22, 5⁰ B) 90⁰ C) 60⁰ D) 15⁰ E) 35⁰

16. (97-11-27) Qo'shni burchaklardan biri ikkinchisidan32⁰ ga katta. Shu burchaklardan kattasini top-

ing.

A) 106⁰ B) 118⁰ C) 116⁰ D) 114⁰ E) 108⁰

17. (98-4-26) A va B nuqtalar orasidagi masofa 500 metrga, B va C nuqtalar orasidagi masofa esa 300

metrga teng. A va C nuqtalar orasidagi masofa

qanchaga teng?

A) 1300 B) 800 C) 200 D) 700 E) aniqlab bo'lmaydi

18. (98-6-32) Bir nuqtadan uchta to'g'ri chiziq o'tkazil gan. Hosil bo'lgan 6 ta burchakning o'zaro ver-

tikal bo'lmagan uchtasi ga teng

ni toping.

A) 270⁰ B) 180⁰ C) 135⁰ D) 100⁰ E) 90⁰

19. (98-6-33) Qo'shni burchaklar bissektrisalari orasidagi burchakni toping.

A) 90⁰ B) 80⁰ C) 100⁰ D) 70⁰ E) 60⁰

20. (98-11-80) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan burchaklarning biri 30⁰ ga teng. Qol-

gan burchaklarni toping.

A) 150⁰; 150⁰; 30⁰ B) 110⁰; 110⁰; 110⁰ C) 60⁰; 60⁰; 30⁰ D) 120⁰; 120⁰; 90⁰ E) 130⁰; 130⁰; 70⁰

21. (99-3-44) AB va CD to'g'ri chiziqlar O nuqtada kesishadi. AOD va COB burchaklarning yig'indisi

230⁰ ga teng. AOC burchakni toping.

A) 70⁰ B) 120⁰ C) 65⁰ D) 95⁰ E) 85⁰

22. (99-4-36) O'ziga qo'shni bo'lgan burchakning qismiga teng burchakni toping.

A) 54⁰ B) 66⁰ C) 72⁰ D) 42⁰ E) 63⁰

23. (99-8-12) O'ziga qo'shni burchakning 44% iga teng

bo'lgan burchakning kattaligini aniqlang.

A) 55⁰ B) 80⁰ C) 60⁰ D) 52⁰ E) 78⁰

24. (00-3-72) Berilgan burchak va unga qo'shni bo'lgan

ikkita burchaklar yig'indisi ga teng. Berilgan

burchakning kattaligini toping.

A) B) C) E) D)

25. (00-5-51) α va β qo'shni burchaklar. Agar bo'lsa, β va α burchaklar ayirmasini toping.

A) 70⁰ B) 60⁰ C) 100⁰ D) 90⁰ E) 80⁰

26. (01-1-64) Uzunligi 4,2 ga teng kesmani 3 : 4 kabi

nisbatda bo'ling.

A) 1,2 va 3 B) 1, 3 va 2,9 C) 1, 4 va 2, 8 D) 1,8 va 2, 4 E) 2 va 2, 2

27. (01-2-38) α va βqo'shni burchaklar. Agar bo'lsa, β va α burchaklar ayirmasini toping.

A) 80⁰ B) 20⁰ C) 60⁰ D) 40⁰ E) 30⁰

28. (01-12-5) Ikkita to'g'ri chiziqning kesishishidan hosil bo'lgan burchaklardan 3 tasining yig'indisi

200⁰. Ularning kattasi kichigidan necha foiz ortiq?

A) 140% B) 80% C) 800% D) 700% E) to'g'ri javob berilmagan

29. (03-6-71) Ikki to'g'ri chiziqning kesishishidan hosil bo'lgan burchaklarning nisbati 5 : 4 ga teng. Shu

burchaklardan kichigini toping.

A) 70⁰ B) 80⁰ C) 60⁰ D) 65⁰ E) 50⁰

30. (03-7-37) O'tkir burchakning sinusi ga teng. Shu burchakka qo'shni burchakning kosinusini toping.