Discussion
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- Question
- In fig., AB || CD, ?a is equal to:
Options- A. 93°
- B. 103°
- C. 83°
- D. 97°
- Correct Answer
- 93°
ExplanationCD || AB (Given)
Produce RQ to meet AB in S
?CRS = ?PSR (at. int. ?s)
But ?CRS = 55°
? ?PSR = 55°
Now in QSP
?QSP + ?QPS + ?PQS = 180°
55° + 38° + ?SQP = 180°
? ?SQP = 180° ? 93° = 87°
But angle a and ?PQS are linear
?a = 180° ? 87°
?a = 93° - 1. Find the measure of an angle, if six times its complement is 12° less than twice its supplement :
Options- A. 48°
- B. 96°
- C. 24°
- D. 58° Discuss
- 2. In the adjoining figure, AB || CD, t is the traversal, EG and FG are the bisectors of ?BEE and ?DFE respectively, then ?EGF is equal to :
Options- A. 90°
- B. 75°
- C. 80°
- D. 110° Discuss
- 3. An angle is equal to one-third of its supplement. Its measure is equal to :
Options- A. 40°
- B. 50°
- C. 45°
- D. 55° Discuss
- 4. In the given, AB || CD. Then X is equal to:
Options- A. 93°
- B. 103°
- C. 83°
- D. 97° Discuss
- 5. The complement of 30°20? is:
Options- A. 69°40?
- B. 59°40?
- C. 35°80?
- D. 159°40? Discuss
- 6. In the following figure, ?B : ?C = 2 : 3, find ?B + ?C.
Options- A. 120°
- B. 52°
- C. 78°
- D. 130° Discuss
- 7. In a ?ABC, if 2?A = 3?B = 6?C, Then ?A is equal to:
Options- A. 60°
- B. 30°
- C. 90°
- D. 120° Discuss
- 8. A, B, C are the three angles of a ?. If A ? B = 15° and B ? C = 30°. Then ?A is equal to :
Options- A. 65°
- B. 80°
- C. 75°
- D. 85° Discuss
- 9. The sides AB and AC of ?ABC have been produced to D and E respectively. The bisectors of ?CBD and ?BCE meet at O. If ?A = 40°, then ?BOC is equal to:
Options- A. 60°
- B. 65°
- C. 75°
- D. 70° Discuss
- 10. In the given figure, DE || BC if AD = 1.7 cm, AB = 6.8 cm and AC = 9 cm, find AE.
Options- A. 2.25cm
- B. 4.5cm
- C. 1.25cm
- D. 2.5cm Discuss
Plane Geometry problems
Search Results
Correct Answer: 48°
Explanation:
Let, the measure of the required angled be A°.
Then, measure of its complement = ( 90 ? A )° measure of its supplement = (180 ? A)°
According to question,
6(90° ? A) = 2(180° ? A) ?12°
? 540° ? 6A = 360° ? 2A ? 12°
? 4A = 192°
? A = 48°.
Correct Answer: 90°
Explanation:
Correct Answer: 45°
Explanation:
Correct Answer: 97°
Explanation:
Through O, draw a line l parallel to both AB and CD. Then
?1 = 45° (alt. ?S)
and ?2 = 30° (alt. ?S)
? ?BOC = ?1 + ?2 = 45° + 30° = 75°
So, X = 360° ? ?BOC = 360° ? 75° = 285°
Hence X = 285°.
Correct Answer: 59°40?
Explanation:
complement of 30°20? = 90° ? ( 30°20? ) = 90° ? ( 30° + 20? )
= (89° ? 30°) + (1° ? 20?)
= 59° + 60? ? 20? [ ? 1° = 60°?]
= 59° + 40? = 59°40?.
Correct Answer: 78°
Explanation:
?DAC = ?B + ?C
(Exterior angle prop. of a ? ABC)
According to question,
130° = 2A + 3A
5A = 130°
A = 26°
? ?B = 52°; ?C = 78°
Correct Answer: 90°
Explanation:
Correct Answer: 80°
Explanation:
Since A, B and C are the angles of a ?,
? A + B + C = 180° .......................................... (1)
According to question,
A ? B = 15° ;
? A = B + 15°....................................................(2)
B ? C = 30°;
? B = C + 30°;...................................................(3)
Put the value of B from equation (2) in Equation (1), we will get
? A = B + 15°
A = C + 30° + 15°
A = C + 45° ........................................................(4)
From a equation,
? A + B + C = 180°
? (C + 45°) + (C + 30°) + C = 180°
? 3C + 45° + 30° = 180°
? 3C = 180° ? 75° = 105°
? C = 35° ..........................................................(5)
From equation (4)
A = C + 45°
Put the value of C from equation (5) , we will get
? ?A = 35° + 45° = 80°.
Correct Answer: 70°
Explanation:
Correct Answer: 2.25cm
Explanation:
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