In a triangle, if the second angle is 5 degree greater than the first angle and the third angle is 5 degree greater than second angle, find the three angles of the triangle.
Answers
Answer: angle A = 55 degree
angle B = 60 degree
angle C = 65 degrees
Step-by-step explanation:
Let angles of the triangle be A , B and C
Let us assume the first angle of the triangle to be 'x'.
According to the condition given in the question we assume the second angle of the triangle to be 'x + 5'.
According to the condition given in the question we assume the third angle of the triangle to be 'x + 10'.
The sum of all the angles of a triangle = 180
Adding all the angles we assumed we get:
=> x + x + 5 + x + 10 = 180
=> 3x + 15 = 180
Taking 15 to the other side of the equation we get:
=> 3x = 180 - 15
=> 3x = 165
Taking 3 to the other side of the equation we get:
=> x = 165 / 3
=> x = 55
Therefore, the value we obtained for 'x' is 55.
Therefore, the value of the first angle of the triangle is 55° because we assumed the first angle of the triangle to be 'x'.
Calculating the value of the second angle of the triangle:
= x + 5
Putting value of 'x' we get:
= 55 + 5
= 60°
Therefore, the value of the second angle of the triangle is 60°.
Calculating the value of the third angle of the triangle:
= x + 10
Putting value of 'x' we get:
= 55 + 10
= 65°
Therefore, the value of the third angle of the triangle is 65°.