The angles of a triangle are in the ratio of 2:6:7 .the complement
Of the smallest angle of the triangle is, explain. Answer=66
To find the complement of an angle, we need to know that the sum of an angle and its complement is always 90 degrees.
Let's assume that the angles of the triangle are 2x, 6x, and 7x, where x is a constant.
According to the given ratio, we know that 2x:6x:7x is equivalent to 2:6:7.
The sum of all angles in a triangle is 180 degrees. So, we can write the equation:
2x + 6x + 7x = 180
Combining like terms, we get:
15x = 180
Dividing both sides by 15, we find:
x = 12
Now, we can substitute the value of x back into the angle measurements:
2x = 2(12) = 24 degrees
6x = 6(12) = 72 degrees
7x = 7(12) = 84 degrees
Now, to find the complement of the smallest angle, we subtract it from 90 degrees:
90 - 24 = 66 degrees
Therefore, the complement of the smallest angle of the triangle is 66 degrees.