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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 the three angles.

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50°, 30 °, 70 °

30°, 40 °, 60 °

50°, 60 °, 70 °

40°, 50 °, 60 °

answer is C.

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Detailed Solution

It is given that the angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is

10 ° .

We know that the sum of all the angles of a triangle

= 180 °

.
Let the first angle be

x

, the second angle be

x + 10 °

and, the third angle be

x + 10 ° + 10 °

.
Hence, we can write that,

x + x + 10 ° + x + 10 ° + 10 ° = 180 °

3 x + 30 ° = 180 °

3 x = 180 ° − 30 °

3 x = 150 °

x = 150 ° 3

x = 50 °

We can calculate the second angle by substituting the value of x in the second angle,

x + 10 ° = 50 ° + 10 ° = 60 °

Similarly, the third angle,

x + 10 ° + 10 ° = 50 ° + 10 ° + 10 ° = 70 °

The first angle is

50 °

, the second angle is

60 °

and the third angle is

70 °

.
Hence, the correct option is 3.

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