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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Mr. Pandit owned 950 gold coins all of which he distributed amongst his three daughters Lalita, Amita and Neeta. Lalita gave 25 gold coins to her husband, Amita donated 15 gold coins and Neeta made jewellery out of 30 gold coins. The new respective ratio of the coins left with them was 20 : 73 : 83. How many gold coins did Amita receive from Mr. Pandit?

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Mr. Pandit owned 950 gold coins all of which he distributed amongst his three daughters Lalita, Amita and Neeta. Lalita gave 25 gold coins to her husband, Amita donated 15 gold coins and Neeta made jewellery out of 30 gold coins. The new respective ratio of the coins left with them was 20 : 73 : 83. How many gold coins did Amita receive from Mr. Pandit?

A380

B415

C400

D350

Nithin ? Aug 13 '2022 at 11:0

Correct answer is: 380

Explanation:

\(20x + 73x + 83x\)

\(= 950 - 25 - 15 - 30\)

\(\implies 176x = 880\)

\(\implies x = \frac{880}{176}=5\)

Therefore, Number of coins got by Amita

\(= \Large 73x+15=73 \times 5+15=380\)

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The ratio between the three angles of a quadrilateral is 1 : 4 : 5 respectively. The value of the fourth angle of the quadrilateral is $60^∘$. 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 : 4 : 5 respectively. The value of the fourth angle of the quadrilateral is $60^∘$. What is the difference between the value of the largest and the smallest angles of the quadrilateral?

A$120^∘ $

B$90^∘$

C$110^∘$

D$100^∘$

Nithin ? Aug 13 '2022 at 10:54

Correct answer is: \(120^∘\)

Explanation:

\(x+ 4x+ 5x+ 60 = 360^∘ \)

\(\implies 10x = 300^∘\)

\(\implies x = 30\)

\(\text{Therefore, Required difference} = 5x - x = 4x\)

\(= \Large 4 \times 30 = 120 ^{\circ}\)

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The ratio between the angles of a quadrilateral is 3 : 4 : 6 : 7. Half the second 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 : 7. Half the second 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$136^∘ $

B$126^∘$

C$94^∘$

D$96^∘$

Nithin ? Aug 13 '2022 at 10:45

Correct answer is: \(126^∘\)

Explanation:

\(3x + 4x + 6x + 7x = \Large 360 ^{\circ}\)

\(= 20x = 360^o\)

\(x = 18^o\)

Therefore, smaller angle of the parallelogram = \(\frac{6x}{2}\)

\(= 3x = 54^∘\)

Therefore, Adjacent angle of parallelogram

\(= 180^∘−54^∘=126^∘\)

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The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?

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The angles of a quadrilateral are in the ratio of 2:4:7:5. The smallest angle of the quadrilateral is equal to the smallest angle of a triangle. One of the angles of the triangle is twice the smallest angle of the triangle. What is the second largest angle of the triangle ?

A80 degrees

B60 degrees

C120 degrees

D40 degrees

Nithin ? Aug 12 '2022 at 22:24

Correct answer is: 60 degrees

Explanation:

Given the angles of a quadrilateral are in the ratio of 2:4:7:5
Let the angles of a quadrilateral are 2x, 4x, 7x, 5x
But we know that sum of the angles = 360 degrees.
=> 2x + 4x + 7x + 5x = 360
=> x = 20
Therfore, the smallest angle of the quadrilateral = 2x = 2x20 = 40 degrees.
One of the angle of the triangle = 2 x 40 = 80 degrees
The other angle is 180 - (40 + 80) = 60 degrees.

Hence the second largest angle of the triangle is 60 degrees.

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