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Answer :

To find \(\angle \)C:

Given:

\(\angle \)B = 45°, \(\angle \)A = 105°

We know that,

Sum of all interior angles in a triangle is 180°.

\(\angle A+\angle B +\angle C = 180° \)

105°+45°+\(\angle \)C = 180°

\(\angle \)C = 180° ? 150°

\(\angle \) C = 30°

So, from the property of triangle, we get \(\angle \)C = 30°

The required triangle can be drawn as follows.

1. Draw a \(\triangle \)ABC with side measures of base BC = 7 cm, \(\angle \)B = 45°, and \(\angle \)C = 30°.

2. Draw a ray BX makes an acute angle with BC on the opposite side of vertex A.

3. Locate 4 points (as 4 is greater in 4 and 3), such as B1, B2, B3, B4, on the ray BX.

4. Join the points B3C.

5. Draw a line through B4 parallel to B3C which intersects the extended line BC at C’.

6. Through C’, draw a line parallel to the line AC that intersects the extended line segment at C’.

7. Therefore, \(\triangle \)A’BC’ is the required triangle.

- Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
- Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are \(\frac{2}{3} \) of the corresponding sides of the first trianngle.
- Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are \(\frac{7}{5} \) of the corresponding sides of the first triangle.
- Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are \(1\frac { 1 }{ 2 }\) times the corresponding sides of the isosceles triangle.
- Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and \(\angle \)ABC=60° ;. Then construct a triangle whose sides are \(\frac{3}4\) of the corresponding sides of the triangle ABC.
- Draw a triangle ABC with side BC = 7 cm, \(\angle \) B=45°, \(\angle \) A=105°;. Then construct a triangle whose sides are \(\frac{4}3 \) times the corresponding sides of \(\triangle \) ABC.
- Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are \(\frac{5}3\)times the corresponding sides of the given triangle.
- Q.1In each of the following, give the justification of the construction also: 1. Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
- Q.2 Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are \(\frac{2}{3} \) of the corresponding sides of the first triangle.
- Q.3 Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are \(\frac{7}{5} \) of the corresponding sides of the first triangle
- Q.4 Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are \(1\frac{1}{2} \) times the corresponding sides of the isosceles triangle.
- Q.5 Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and \(\angle \)ABC = 60°. Then construct a triangle whose sides are \(\frac{3}{4} \) of the corresponding sides of the triangle ABC.
- Q.7 Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are \(\frac{5}{3} \) times the corresponding sides of the given triangle.

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