One of the angles of a quadrilateral is thrice the smaller angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 4:5. Remaining three angles of the quadrilateral are in ratio 4 : 11 : 9 respectively. What is the sum of the largest and the smallest angles of the quadrilateral?

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One of the angles of a quadrilateral is thrice the smaller angle of a parallelogram. The respective ratio between the adjacent angles of the parallelogram is 4:5. Remaining three angles of the quadrilateral are in ratio 4 : 11 : 9 respectively. What is the sum of the largest and the smallest angles of the quadrilateral?

A$255^∘ $

B$260^∘$

C$265^∘$

D$270^∘$

Nithin ? Aug 13 '2022 at 20:53

Correct answer is: \(260^∘\)

Explanation:

 

For the Parallelogram,  \(\Large 4x ^{\circ} + 5x ^{\circ} = 180 ^{\circ}\)

\(=> 9x = 180 \implies x = \frac{180}{9} = 20\)

=> smaller angle of parallelogram = \(\Large 4 \times 20 = 80^o\)

Therefore, One angle of the quadrilateral = \(\Large 3 \times 80 = 240^o\)

Now. 4y + 11y + 9y

= 360 - 240 = 120

\(= 24y = 120 \implies y = \frac{120}{24} = 5 \)

=> Its smallest angle

\(= \Large 4 \times 5 = 20^o\)

Therefore, Required sum = \(\Large 240 ^{\circ} + 20 ^{\circ} = 260 ^{\circ}\)

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The largest and the smallest angles of a triangle are in the ratio of 3 : 1 respectively. The second largest angle of the triangle is equal to 44°. What is the value of 150 per cent of the largest angle of the triangle ?

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The largest and the smallest angles of a triangle are in the ratio of 3 : 1 respectively. The second largest angle of the triangle is equal to 44°. What is the value of 150 per cent of the largest angle of the triangle ?

A149

B 129

C 153

D 173

Nithin ? Aug 13 '2022 at 20:16

Correct answer is: 153

Explanation:

 

If the largest & smallest angles are 3x & x respectively, then

 

\(3x+x+44= 180\), \( x=\frac{136}{4}=34\)

 

Three angles are 34, 102 & 44

 

So 150 per cent of the largest angle= \(102 \times \frac{150}{100}= 153\)

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One of the angles of a triangle is two-third of sum of adjacent angles of parallelogram. Remaining angles of the triangle are in ratio 5 : 7 respectively. What is the value of second largest angle of the triangle?

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One of the angles of a triangle is two-third of sum of adjacent angles of parallelogram. Remaining angles of the triangle are in ratio 5 : 7 respectively. What is the value of second largest angle of the triangle?

A$25^∘$

B$40^∘$

C$35^∘$

DCannot be determined

Nithin ? Aug 13 '2022 at 20:7

Correct answer is: \(35^∘\)

Explanation:

Sum of adjacent angles of a parallelogram = \(180^o\)

Therefore, One of the angles of triangle

\(=\Large \frac{2}{3} \times 180 ^{\circ} = 120 ^{\circ}\)

Sum of three angles of a triangle = \(180^o\)

Therefore, 5x + 7x = 180 - 120

=> 12x = 60 => x = 5

 

Second angle of triangle =  \(\Large 5 \times 5 = 25 ^{\circ}\)

Third angle of triangle = \(\Large 7 \times 5 = 35 ^{\circ}\)

The second largest angle of triangle = \(35^o\)

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The ratio between the adjacent angles of a parallelogram is 2 : 3 respectively. Half the smaller angle of the parallelogram is equal to the smallest angle of a quadrilateral. Largest angle of quadrilateral is four times its smallest angle. What is the sum of largest angle of quadrilateral and the smaller angle of parallelogram?

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BANK PO Exam (Union Bank of India) 2001 click here to view all questions

The ratio between the adjacent angles of a parallelogram is 2 : 3 respectively. Half the smaller angle of the parallelogram is equal to the smallest angle of a quadrilateral. Largest angle of quadrilateral is four times its smallest angle. What is the sum of largest angle of quadrilateral and the smaller angle of parallelogram?

A$252^∘$

B$226^∘$

C$144^∘$

DNone of these

Nithin ? Aug 13 '2022 at 13:6

Correct answer is: None of these

Explanation:

Let the adjacent angles of parallelogram be \(\Large 2x ^{\circ} \text{ and }\ 3x ^{\circ}\) respectively
Then, \(\Large 2x ^{\circ} + 3x ^{\circ} = 180^o\)

\(\Large 5x ^{\circ} = 180^o\)

\(x^∘=36^∘ \)

 

Smaller angle of parallelogram \(= 2x = 72^∘\)

= Smallest angle of the quadrilateral \(= 36^∘\)

 

Therefore, Its largest angle \(= 4×36=144^∘\)

 

Therefore, Required sum \(= 144 + 72 = 216^∘\)

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Rohit has some 50 paisa coins, some 2 rupee coins, some 1 rupee coins and some 5 rupee coins. The value of all the coins is Rs 50. Number of 2 rupee coins is 5 more than that of the 5 rupee coins. 50 paisa coins are double in number than 1 rupee coins Value of 50 paisa coins and 1 rupee coins is Rs 26. How many 2 rupee coins does he have ?

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Rohit has some 50 paisa coins, some 2 rupee coins, some 1 rupee coins and some 5 rupee coins. The value of all the coins is Rs 50. Number of 2 rupee coins is 5 more than that of the 5 rupee coins. 50 paisa coins are double in number than 1 rupee coins Value of 50 paisa coins and 1 rupee coins is Rs 26. How many 2 rupee coins does he have ?

A4

B2

C7

DCannot be determined

Nithin ? Aug 13 '2022 at 12:51

Correct answer is: 7

Explanation:

Let he has X number of 2 ruppee coins.
No. of 5 ruppee coins = X -5
Value of 1 ruppe and 50 paisa coins = Rs. 26

The Value of all Coins = Rs. 50
2*X + 5*(X-5) +26 = 50

2X +5X - 25 = 50 - 26
7X = 24 +25

X = 49/7 = 7
No. of 2 ruppee coins = 7.

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The ratio between the angles of a quadrilateral is 3 : 4 : 6 : 5. Two-third of the largest angle of the quadrilateral is equal to the smaller angle of a parallelogram. What is the value of adjacent angle of the parallelogram ?

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The ratio between the angles of a quadrilateral is 3 : 4 : 6 : 5. Two-third of the largest angle of the quadrilateral is equal to the smaller angle of a parallelogram. What is the value of adjacent angle of the parallelogram ?

A$120^°$

B $110^°$

C$100^°$

D $130^°$

Nithin ? Aug 13 '2022 at 12:19

Correct answer is: \(100^°\)

Explanation:

Smaller angle of parallelogram

\(= \frac{6}{18} \times 360 \times \frac{2}{3}\)

\(= 80 ^o\)

\(\text{Adjacent angle of parallelogram = 180°– 80° = 100°}\)

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The ratio between the three angles of a quadrilateral is 1 : 6 : 2 respectively. The value of the fourth angle of the quadrilateral is $45^∘$. What is the difference between the value of the largest and the smallest angles of the quadrilateral?

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The ratio between the three angles of a quadrilateral is 1 : 6 : 2 respectively. The value of the fourth angle of the quadrilateral is $45^∘$. What is the difference between the value of the largest and the smallest angles of the quadrilateral?

A$165^∘$

B $140^∘$

C$175^∘$

D$150^∘$

Nithin ? Aug 13 '2022 at 12:6

Correct answer is: \(175^∘\)

Explanation:

Sum of the angles of quadrilateral = \(\Large 360 ^{\circ}\)

\(\implies x + 6x + 2x + 45 = 360\)

\(\implies 9x = 360 - 45 = 315 \)

\(\implies x = \Large \frac{315}{9} =35\)

Therefore, Required difference = \(6x - x = 5x\)

\(= \Large 5 \times 35 - 175 ^{\circ}\)

\(= \Large 175 ^{\circ}\)

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