Plane Geometry problems
- 1. 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
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
- 2. The complement of 30°20? is:
Options- A. 69°40?
- B. 59°40?
- C. 35°80?
- D. 159°40? Discuss
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?.
- 3. In the given, AB || CD. Then X is equal to:
Options- A. 93°
- B. 103°
- C. 83°
- D. 97° Discuss
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°.
- 4. 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
Correct Answer: 45°
Explanation:
- 5. 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
Correct Answer: 90°
Explanation:
- 6. 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
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°.
- 7. In fig., AB || CD, ?a is equal to:
Options- A. 93°
- B. 103°
- C. 83°
- D. 97° Discuss
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°
- 8. In the following figure, ?B : ?C = 2 : 3, find ?B + ?C.
Options- A. 120°
- B. 52°
- C. 78°
- D. 130° Discuss
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°
- 9. 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
Correct Answer: 90°
Explanation:
- 10. 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
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°.
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