The ratio between the adjacent angles of a parallelogram is 7 : 8 respectively. Also the ratio between the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of parallelogram and second largest angle of the quadrilateral?

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The ratio between the adjacent angles of a parallelogram is 7 : 8 respectively. Also the ratio between the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of parallelogram and second largest angle of the quadrilateral?

A168°

B228°

C156°

D224°

Nithin ? Aug 14 '2022 at 11:8

Correct answer is: 168°

Explanation:

 

Let the adjacent angles be \(7x^∘\text{and }8x^∘\)

Therefore, 7x + 8x = 180

=> 15x = 180

=> x = 12

Therfore, Smaller angle = 7 x 12 = 84°

Again. 5y + 6y + 7y + 12y = 360°

=> 30y = 360°

= y = \(\frac{360}{30}\)

Therefore, Second largest angle of the quadrilateral

= 7×12 = \(84^o\)

 

Therefore, Required sum = \(84 + 84 = 168^o\)

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The ratio between the three angles of a quadrilateral is 13 : 9 : 5 respectively. The value of the fourth angle of the quadrilateral is 36∘C. What is the difference between the largest and the second smallest angles of the quadrilateral?

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The ratio between the three angles of a quadrilateral is 13 : 9 : 5 respectively. The value of the fourth angle of the quadrilateral is 36∘C. What is the difference between the largest and the second smallest angles of the quadrilateral?

A104°

B 108°

C72°

D 96°

Nithin ? Aug 14 '2022 at 10:10

Corect answre is: 96°

Explanation:

Let the three angles of quadrilateral be

\(13x^∘, 9x^∘,\text{ and }5x^∘ \text{ respectively.}\)

\(\text{Therefore, } 13x + 9x + 5x = 360 - 36\)

\(\implies 27x = 324 \implies x = \frac{324}{27} =12\)

Therefore, Required difference

\(=13x - 5x = 8x = 8\times \text{12 }= 96^∘\)

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The largest and the second largest angles of a triangle are in the ratio of 4 : 3 respectively. The smallest angle is half the largest angle. What is the difference between the smallest and the largest angles of the triangle?

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The largest and the second largest angles of a triangle are in the ratio of 4 : 3 respectively. The smallest angle is half the largest angle. What is the difference between the smallest and the largest angles of the triangle?

A30°

B60°

C40°

D20°

Nithin ? Aug 13 '2022 at 21:46

Correct answer is: 40°

Explanation:

The smallest angle of triangle is half of the largest angle.

Therefore, Ratio of three angles = 4 : 3 : 2

 

Now, 4x + 3x + 2x = \(180^o\)

\(\implies 9x = 180 \implies x = 20\)

Therefore, Required difference = 4x - 2x = 2x = \(\Large 2 \times 20 = 40^o\)

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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?

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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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