The angles of a triangle in ascending order are x, y and z. If y - x = z - y = 10°, then find the angles of the triangle.

Given, The three angles of the triangle in ascending order are x, y, and z. Given, ⇒ y − x = 10° ⇒ y = 10° + x ....(1) Given, ⇒ z − y = 10° ....(2) Substitute value of y from equation (1) in (2), we get : ⇒ z − y = 10° ⇒ z - (10° + x) = 10° ⇒ z = 10° + 10° + x ⇒ z = 20° + x. So, the three angles of the triangle in terms of x are: First angle: x Second angle: x + 10° Third angle: x + 20° We know that, The sum of the angles in any triangle is always 180°. ⇒ x + y + z = 180° ⇒ x + (x + 10°) + (x + 20°) = 180° ⇒ 3x + 30° = 180° ⇒ 3x = 180° − 30° ⇒ 3x = 150° ⇒ x = ⇒ x = 50°. Substituting the value of x, ⇒ y = x + 10° = 50° + 10° = 60° ⇒ z = x + 20° = 50° + 20° = 70°. Hence, x = 50°, y = 60°, z = 70°.

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A shopkeeper sold a table and a chair for ₹ 1,050, thereby making a profit of 10% on the table and 25% on the chair. If he had taken a profit of 25% on the table and 10% on the chair, then he would have got ₹ 1,065. What is the cost price of 1 table and 1 chair.

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A boatman rowing at the rate of 5 km/hr in still water takes thrice as much time in going 40 km upstream as in going 40 km downstream. What is the speed of the stream?

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A shopkeeper buys pens and pencils at ₹ 5 and ₹ 1 per price respectively. For every two pens, he buys three pencils. He sold pens and pencils at 12% and 10% profit respectively. If his total sale is ₹ 725, then find the number of pens and pencils sold by him.

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Mathematics

The angles of a triangle in ascending order are x, y and z. If y - x = z - y = 10°, then find the angles of the triangle.

Linear Equations

Related Questions

A shopkeeper sold a table and a chair for ₹ 1,050, thereby making a profit of 10% on the table and 25% on the chair. If he had taken a profit of 25% on the table and 10% on the chair, then he would have got ₹ 1,065. What is the cost price of 1 table and 1 chair.

A boatman rowing at the rate of 5 km/hr in still water takes thrice as much time in going 40 km upstream as in going 40 km downstream. What is the speed of the stream?

A shopkeeper buys pens and pencils at ₹ 5 and ₹ 1 per price respectively. For every two pens, he buys three pencils. He sold pens and pencils at 12% and 10% profit respectively. If his total sale is ₹ 725, then find the number of pens and pencils sold by him.