Question
Using ruler and compasses, construct the following angle:
37.5°
37.5°
✓
Answer
Steps of Construction:
(i) Draw a line segment $B C$.
(ii) With centre $B$ and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and same radius cut off $\operatorname{arcs} P Q$ and $Q R$.
(iv) Now bisect arc QR at $S$ and again bisect arc QS at T.
(v) Bisect arc PT at K.
(vi) Join $B K$ and produce it to $A$.
Then, $\angle A B C=37 \frac{1}{2}^{\circ}$ or 37.5 .
(i) Draw a line segment $B C$.
(ii) With centre $B$ and some suitable radius, draw an arc meeting $B C$ at $P$.
(iii) With centre $P$ and same radius cut off $\operatorname{arcs} P Q$ and $Q R$.
(iv) Now bisect arc QR at $S$ and again bisect arc QS at T.
(v) Bisect arc PT at K.
(vi) Join $B K$ and produce it to $A$.
Then, $\angle A B C=37 \frac{1}{2}^{\circ}$ or 37.5 .
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→Kunal pulled out a string from one of his shoes. He found that it was 66 cm long. He bent it into different shapes one by one.
Q.1. If Kunal formed an equilateral triangle from the shoe string, what will be the length of each side of the triangle formed ?
(a) 11 cm $\quad$$\quad$(b) 13 cm$\quad$$\quad$(c) 22 cm$\quad$$\quad$(d) 33 cm
Q.2. If he formed a square from the string, the area of the square would be :
(a) $212.5 cm^2$$\quad$$\quad$ (b) $272.25 cm^2$ $\quad$$\quad$(c) $312.75 cm^2$$\quad$$\quad$ (d) $324 cm^2$
Q.3. He formed a circle from the string. Find the radius of the circle formed. [Use $\pi \frac{22}{7}$ ]
(a) 7 cm $\quad$$\quad$(b) 7.5 cm $\quad$$\quad$(c) 9 cm$\quad$$\quad$ (d) 10.5 cm
Q.4. The area of the circle formed from the string will be : [Use $\pi \frac{22}{7}$ ]
(a) $272.25 cm^2$$\quad$$\quad$(b) $346.5 cm^2$ $\quad$$\quad$(c) $414.75 cm^2$ $\quad$$\quad$(d) $452 cm^2$
→Q.1. If Kunal formed an equilateral triangle from the shoe string, what will be the length of each side of the triangle formed ?
(a) 11 cm $\quad$$\quad$(b) 13 cm$\quad$$\quad$(c) 22 cm$\quad$$\quad$(d) 33 cm
Q.2. If he formed a square from the string, the area of the square would be :
(a) $212.5 cm^2$$\quad$$\quad$ (b) $272.25 cm^2$ $\quad$$\quad$(c) $312.75 cm^2$$\quad$$\quad$ (d) $324 cm^2$
Q.3. He formed a circle from the string. Find the radius of the circle formed. [Use $\pi \frac{22}{7}$ ]
(a) 7 cm $\quad$$\quad$(b) 7.5 cm $\quad$$\quad$(c) 9 cm$\quad$$\quad$ (d) 10.5 cm
Q.4. The area of the circle formed from the string will be : [Use $\pi \frac{22}{7}$ ]
(a) $272.25 cm^2$$\quad$$\quad$(b) $346.5 cm^2$ $\quad$$\quad$(c) $414.75 cm^2$ $\quad$$\quad$(d) $452 cm^2$
Find the S.I. and amount on: Rs. 850 from 10th March to 3rd August at $2 \frac{1}{2} \%$ p.a.
→Prove that:
(i) $\triangle A B C \cong \triangle A D C$
(ii) $\angle B=\angle D$
(iii) $A C$ bisects angle $D C B$
→(i) $\triangle A B C \cong \triangle A D C$
(ii) $\angle B=\angle D$
(iii) $A C$ bisects angle $D C B$