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- Question
- 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°
- Correct Answer
- 48°
ExplanationLet, 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°. - 1. 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
- 2. 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
- 3. In the given, AB || CD. Then X is equal to:
Options- A. 93°
- B. 103°
- C. 83°
- D. 97° Discuss
- 4. The complement of 30°20? is:
Options- A. 69°40?
- B. 59°40?
- C. 35°80?
- D. 159°40? Discuss
- 5. Two angles are supplementary and the ratio of the angels is 1:4. what is the value of smaller angle?
Options- A. 36 degree
- B. 45 degree
- C. 35 degree
- D. 72 degree Discuss
- 6. In fig., AB || CD, ?a is equal to:
Options- A. 93°
- B. 103°
- C. 83°
- D. 97° Discuss
- 7. In the following figure, ?B : ?C = 2 : 3, find ?B + ?C.
Options- A. 120°
- B. 52°
- C. 78°
- D. 130° Discuss
- 8. 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
- 9. 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
- 10. 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
Plane Geometry problems
Search Results
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: 36 degree
Explanation:
As we know that the angles are supplementary so sum of angles will be 180 degree.
Let us assume that the ratio factor is r.
According to question,
Angles are supplementary and have a ratio of 1:4.
r + 4r = 180
? 5r = 180
? r = 180/5
? r = 36
Correct Answer: 93°
Explanation:
CD || 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°
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:
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