2. Simplify [25 x t-4]/[5-3 x 10 x t-8]
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?
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.
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°
4. In the Figure, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.
[Hint: Draw a line parallel to ST through point R.]
3. In the Figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.
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°
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).
In the Figure, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
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.
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.
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.
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