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Prove that an equilateral triangle can be constructed on any given line segment.

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Draw 60 degree angle at the both end of line segment and then draw angle bisector of that two line of 60 degree and then join the three point which is generated by above procedure.
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The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°, find all the three angles.
Let the any one of the angle of triangle be x then other two angle are x+10, x+20 According to Question, x + (x+10) + (x+20)=180 3x + 30 = 180 3x = 150 x = 50 Thus, angles would be 50, 60, and 70.
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Given that HCF (161,345) = 23, find their LCM.
N¹ *N² = LCM * HCF 161 *345 =23 * N² N² =2415
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A triangular park has sides 120 m, 80 m and 50 m. A gardener has to put a fence all around it and also plant grass inside. How much area does he need to plant? Find the cost of fencing it with barbed wire at the rate of Rs. 20 per metre, leaving a space of 3 m wide for a gate on one side.
Perimeter of the garden=120+80+50 =250m As space of 3 m wide for a gate is left on one side, so the length of wire required =(250-3)=247m. Cost of fencing=247X20=Rs 4940. semiperimeter(s)=perimeter/2...
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