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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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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Twenty five percent of Pranab’s annual salary is equal to eighty percent of Surya’s annual salary. Surya’s monthly salary is forty percent of Dheeru’s monthly salary. If Dhreeu’s annual salary is Rs 6 lacs, what is Pranab’s monthly salary ? (At some places annual income and in some place monthly income are given)

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Twenty five percent of Pranab’s annual salary is equal to eighty percent of Surya’s annual salary. Surya’s monthly salary is forty percent of Dheeru’s monthly salary. If Dhreeu’s annual salary is Rs 6 lacs, what is Pranab’s monthly salary ? (At some places annual income and in some place monthly income are given)

ARs 7.68 lacs

BRs 56,000

CRs 8.4 lacs

D Rs 64,000

Nithin ? Aug 13 '2022 at 11:52

Correct answer is: Rs 64,000

Explanation:

\(\text{Dhreeu’s monthly salary} = \frac{6,00,000 }{12}= \text{Rs. 50,000}\)

\(\text{Surya’s monthly salary} = 50,000 \times \frac{40}{100} = \text{Rs. 20,000}\)

\(\text{Pranab’s monthly salary} = 20,000 \times \frac{80}{25} = \text{Rs. 64,000}\)

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The largest and the second largest angles of a triangle are in the ratio of 13 : 12 respectively. The smallest angle is 20% of the sum of the largest and the second largest angles. What is the sum of the smallest and the second largest angles ?

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The largest and the second largest angles of a triangle are in the ratio of 13 : 12 respectively. The smallest angle is 20% of the sum of the largest and the second largest angles. What is the sum of the smallest and the second largest angles ?

A$120^°$

B $108^°$

C$100^°$

D$102^°$

Nithin ? Aug 13 '2022 at 11:9

Correct answer is: \(102^°\)

Explanation:

Smallest angle

\(= (13+12)\times\frac{20}{100}=5\)

Ratio of angles = 13 : 12: 5

Sum of smallest and second largest angles

\(=\frac{180 \times(12 +5)}{(13+12+5)}\)

\(=\frac{180 \times 17}{30}\)

\(= 102^o\)

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