Discussion
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- Question
- In ?ABC, the angle bisectors of ?B and ?C meet at O. If ?A = 70°, then ?BOC is equal to:
Options- A. 135°
- B. 125°
- C. 115°
- D. 110°
- Correct Answer
- 125°
Explanation
- 1. In the adjoining figure ?A + ?B + ?C + ?D + ?E + ?F =?
Options- A. 270°
- B. 300°
- C. 360°
- D. 330° Discuss
- 2. In the given figure, AB || DC, find the value of x.
Options- A. x = 8
- B. x = 9
- C. x = 8 or 9
- D. x = 10 Discuss
- 3. In an equilateral ? ABC, if AD ? BC, then which option is true?
Options- A. 3AB2 = 2AD2
- B. 2AB2 = 3AD2
- C. 3AB2 = 4AD2
- D. 4AB2 = 3AD2 Discuss
- 4. D and E are the points on the sides AB and AC respectively of ?ABC such that AD = 8 cm, BD = 12 cm, AE = 6 cm and EC = 9 cm. Then find BC/ DE.
Options- A. 5 2
- B. 2 5
- C. 5 7
- D. 5 3 Discuss
- 5. A ladder 15 m long reaches a window which is 9 m above the ground on one side of street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. What is the width of the street:
Options- A. 31 m
- B. 12 m
- C. 30 m
- D. 21 m Discuss
- 6. The complement of an angle exceeds the angle by 60°. Then the angle is equal to:
Options- A. 25°
- B. 30°
- C. 15°
- D. 35° Discuss
- 7. In the given figure, AB || CD and AC || BD. If ?EAC = 40°, ?FDG = 55°, ?HAB = x; then the value of x is:
Options- A. 95°
- B. 70°
- C. 35°
- D. 85° Discuss
- 8. In the given figure, OP bisect ?BOC and OQ bisects ?AOC. Then ?POQ is equal to :
Options- A. 90°
- B. 120°
- C. 60°
- D. 100° Discuss
- 9. If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose a:
Options- A. Trapezium
- B. Rectangle
- C. Square
- D. circle Discuss
- 10. In the given figure, ?B = ?C = 55° and ?D = 25°. Then:
Options- A. BC < CA < CD
- B. BC > CA > CD
- C. BC < CA, CA > CD
- D. BC > CA, CA < CD Discuss
Plane Geometry problems
Search Results
Correct Answer: 360°
Explanation:
In ?ACE
?A + ?C + ?E = 180°
Similarly in ?DFB
?D + ?F + ?B = 180°
? (?A + ?C + ?E) + (?D + ?F + ?B) = 360°
?A + ?B + ?C + ?D + ?E + ?F = 360°
Correct Answer: x = 8 or 9
Explanation:
Correct Answer: 3AB2 = 4AD2
Explanation:
Correct Answer: 5 2
Explanation:
Correct Answer: 21 m
Explanation:
Draw a figure as per given question,
In a Right triangle ADC, Use the (Pythagoras Theorem)
AC = ?DC2 - AD2
? AC = ? 152 - 9 2
? AC = ? 225 - 81
? AC = ? 144
? AC = 12 cm
In a Right triangle BCE, Use the formula
CB = ? CD2 - BE2
? CB = ?15 2 - 122
? CB = ?225 - 144
? CB = ? 81
? CB = 9 m
? Width of the street (AC + BC) = AB = 12 + 9 = 21 m.
Correct Answer: 15°
Explanation:
Let, the angle be A
? Its complement angle = 90° ? A
According to the question
(90 ? A) = A + 60°
? 90 - 60 = A + A
? 2A = 30°
? A = 15°
Correct Answer: 85°
Explanation:
?DCK = ?FDG = 55° (corr. ?s)
? ?ACE = ?DCK = 55° (vert. opp. ?s)
So, ?AEC = 180° ? (40° + 55°) = 85°
? ?HAB = ?AEC = 85° (corr. ?s)
Hence, x = 85°.
Correct Answer: 90°
Explanation:
Since OP bisects ?BOC,
? ?BOC = 2?POC
Again, OQ bisects ?AOC,
? ?AOC = 2?QOC
Since ray OC stands on line AB, ?,
?AOC + ?BOC = 180°
? 2?QOC + 2?POC = 180°
? 2?QOC + ?POC = 180°
? ?QOC + ?POC = 90°
? ?POQ = 90°.
The above sum can also be restated as follows; The angle between the bisectors of a linear pair of angles is a right angle.
Correct Answer: Rectangle
Explanation:
Correct Answer: BC > CA, CA < CD
Explanation:
According to question,
?B = ?C = 55° , ?D = 25°
We can say ,
AB = AC ( ? ?B = ?C = 55° )
In Triangle ABC,
?A + ?B + ?C = 180°
? ?A + 55° + 55° = 180°
? ?A + 110° = 180°
? ?A = 180° - 110°
? ?A = 70° ..........................(1)
As per given figure,
?ACD + ?ACB = 180° ( ?ACB = ?C = 55°)
? ?ACD + 55° = 180°
? ?ACD = 180° - 55°
? ?ACD = 125° ....................... (2)
Now in Triangle ACD,
?CAD + ?ACD + ?CDA = 180°
? ?CAD + 125° + 25° = 180°
? ?CAD + 150° = 180°
? ?CAD = 30° ...........................(3)
( In a ?, greater angle has longer side opposite to it )
From the equation (1) , (2) and (3);
?B < ?A and ?CAD > ?D ;
? BC > CA and CA < CD
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