In a triangle, if the second angle is 3 times the sum of the first angle and 3 and the third angle is the sum of 2 times the first angle and 3, find the three angles of the triangle.
Answers
Let us assume the first angle of the triangle to be 'x'.
We can assume the second angle of the triangle according to the condition given in the question as 3(x + 3).
We can also assume the third angle of the triangle according to the condition given in the question as 2x + 3.
Sum of all the angles of a triangle we know = 180°
Adding all the values we assumed together and equating it to 180:
=> x + 3(x + 3) + 2x + 3 = 180
=> x + 3x + 9 + 2x + 3 = 180
=> 4x +12 + 2x = 180
=> 6x + 12 = 180
Taking 12 to the other side of the equation we get:
=> 6x = 180 - 12
=> 6x = 168
Taking 6 to the other side of the equation we get:
=> x = 168 / 6
=> x = 28
Therefore, the value we obtained for 'x' is 28.
Therefore, the value of the first angle we assumed as 'x' is 28°.
Calculating the value of the second angle which we assumed:
= 3(x + 3)
Putting value of x:
= 3(28 + 3)
= 3(31)
= 93°
Therefore, the value of the second angle of the triangle is 93°
Calculating the value of the third angle which we assumed:
= 2x + 3
Putting the value of x:
= 2 x 28 + 3
= 56 + 3
= 59°
Therefore, the value of the third angle of the triangle is 59°.
Step-by-step explanation:
third angle is 59
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