The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

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The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

A160°

B 180°

C190°

D 170°

Nithin ? Aug 13 '2022 at 21:14

Correct answer is: 180°

Explanation:

Sum of the angles of a quadrilateral  = 360

Therefore, \(3x + 4x + 5x + 6x = 360\)

\(\implies 18x = 360\)

\(\implies x = \frac{360}{18}= 20\)

Therefore, smallest angle of quadrilateral \( = 3×20 = 60\)
 Largest angle of quadrilateral \(= 6×20 = 120\)

Therefore, smallest angle of triangle \(= 60× \frac{2}{3}=40\)

Largest angle of triangle \(= 2×40 = 80\)

Therefore, third angle of triangle \(= 180−40−80=60\)

Required sum \(= 60 +120 = 180\)

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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?

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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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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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