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RS Aggarwal - Mathematics

3. Linear Equations in Two Variables

1. Real Numbers
2. Polynomials
3. Linear Equations in Two Variables
Triangles
5. Trigonometric Ratios
6. T-Ratios of Some Particular Angles
7. Trigonometric Ratios of Complementary Angles
8. Trigonometric Identities
10. Quadratic Equations
9. Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive
11. Arithmetic Progression
12. Circles
13. Constructions
14. Heights and Distances
15. Probability
16. Coordinate Geometry
17. Perimeter and Area of Plane Figures
18. Area of Circle, Sector and Segment
19. Volume and Surface Area of Solids
20. Summative Assessment I
21. Summative Assessment II

Exercise 3A

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Exercise 3B

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Exercise 3C

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Exercise 3D

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Exercise 3E

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Exercise 3F

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Multiple Choice Questions (MCQ)

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Formative Assessment (Unit Test)

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Q. 214.2( 5 Votes )

In a cyclic quadrilateral ABCD, it is being given that ∠A = (x + y + 10)°, ∠B = (y + 20)°, ∠C = (x + y – 30)° and ∠D = (x + y)°. Then, ∠B = ?
A. 70°

B. 80°

C. 100°

D. 110°

Class 10th RS Aggarwal - Mathematics 3. Linear Equations in Two Variables

Answer :

It is given in the question that,

In cyclic quadrilateral ABCD, we have:

∠ A = (x + y + 10)^o

∠ B = (y + 20)^o

∠ C = (x + y – 30)^o

∠ D = (x + y)^o

As ABCD is a cyclic quadrilateral

∴ ∠ A + ∠ C = 180^o and ∠ B + ∠ D = 180^o

Now, ∠ A + ∠ C = 180^o

(x + y + 10)^o + (x + y – 30)^o = 180^o

2x + 2y – 20^o = 180^o

x + y = 100^o (i)

Also, ∠ B + ∠ D = 180^o

(y + 20)^o + (x + y)^o = 180^o

x + 2y + 20^o = 180^o

x + 2y = 160^o (ii)

On subtracting (i) from (ii), we get

y = (160 – 100)^o

y = 60^o

Putting the value of y in (i), we get

x + 60^o = 100^o

x = 100^o – 60^o

x = 40^o

∴ ∠ B = (y + 20)^o

∠ B = 60^o + 20^o = 80^o

Hence, option B is correct

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