TOP QUESTIONS AND ANSWERS FOR YOU

Maths

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8th

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February 24, 2022

**1.If a new-born bear weighs 4 kg, calculate how many kilograms a five-year-old bear weigh if its weight increases by the power of 2 in 5 years?**

David Miller

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Student

Maths

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9th

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February 24, 2022

5. **In Fig. 6.40, ∠X = 62°, ∠XYZ = 54°. If YO and ZO are the bisectors of ∠XYZ and ∠XZY respectively of Δ XYZ, find ∠OZY and ∠YOZ.**

Joslin Smith

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Student

As we know, the sum of the interior angles of the triangle is 180°.

So, ?X +?XYZ + ?XZY = 180°

substituting the values as given in the question we get,

62° + 54° + ?XZY = 180°

Or, ?XZY = 64°

Now, As we know, ZO is the bisector so,

?OZY = ½ ?XZY

? ?OZY = 32°

Similarly, YO is a bisector and so,

?OYZ = ½ ?XYZ

Or, ?OYZ = 27° (As ?XYZ = 54°)

Now, as the sum of the interior angles of the triangle,

?OZY +?OYZ + ?O = 180°

Substituting their respective values we get,

?O = 180° – 32° – 27°

Or, ?O = 121°

Maths

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9th

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February 24, 2022

4. **In the Figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.**

Joslin Smith

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Student

Maths

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9th

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February 24, 2022

3. **In the Figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE**.

Joslin Smith

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Student

Solution:

Since AB || CD GE is a transversal.

It is given that ?GED = 126°

So, ?GED = ?AGE = 126° (alternate interior angles)

Also,

?GED = ?GEF + ?FED

As

EF ? CD, ?FED = 90°

? ?GED = ?GEF + 90°

Or, ?GEF = 126° – 90° = 36°

Again, ?FGE + ?GED = 180° (Transversal)

Substituting the value of ?GED = 126° we get,

?FGE = 54°

So,

?AGE = 126°

?GEF = 36° and

?FGE = 54°

Maths

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9th

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February 24, 2022

2. **In the Figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ROS = 1/2(∠QOS – ∠POS).**

Joslin Smith

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Student

Maths

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9th

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February 24, 2022

**In the Figure, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.**

Joslin Smith

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Student

Maths

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8th

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February 23, 2022

6. **From a circular sheet of radius 4 cm, a circle of radius 3 cm is cut out. Calculate the area of the remaining sheet after the smaller circle is removed.**

Joslin Smith

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Student

Maths

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8th

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February 23, 2022

4. **The area of a rhombus is 16 cm2 and the length of one of its diagonal is 4 cm. Calculate the length of other diagonal.**

Joslin Smith

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Student

Maths

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8th

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February 23, 2022

3. **A lawnmower takes 750 complete revolutions to cut grass on a field. Calculate the area of the field if the diameter of the lawnmower is 84 cm and the length is 1 m.**

Joslin Smith

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Student

Maths

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8th

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February 23, 2022

2. ** Calculate the height of a cuboid which has a base area of 180 cm2 and volume is 900 cm3.**

Joslin Smith

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Student

Volume of cuboid = base area × height

900 = 180 × height

So, height = 900/180 = 5 cm