the three angles of a triangle are 3x,x+10, and 2x-40. Find the size of the smallest angle in a triangle
recall that the sum of the interior angles of any triangle is 180 degrees,, thus:
3x + (x+10) + (2x-40) = 180
6x - 30 = 180
6x = 210
x = 35
therefore, the angles are:
3x = 3(35) = 105
x+10 = 35+10 = 45
2x-40 = 2(35)-40 = 30
..and the smallest angle is 30 degrees
so there,, :)
To find the size of the smallest angle in a triangle, we need to know the values of 'x'.
Let's add up the three angles of the triangle and set the sum equal to 180 degrees (since the sum of the angles in a triangle is always 180 degrees).
(3x) + (x + 10) + (2x - 40) = 180
Simplifying the equation:
6x - 30 = 180
Next, let's solve for 'x':
6x = 180 + 30
6x = 210
Dividing both sides by 6:
x = 210 / 6
x = 35
Now that we have the value of 'x', we can substitute it back into the expressions for the angles to find their values:
Angle 1 = 3x = 3 * 35 = 105 degrees
Angle 2 = x + 10 = 35 + 10 = 45 degrees
Angle 3 = 2x - 40 = 2 * 35 - 40 = 30 degrees
Therefore, the smallest angle in the triangle is 30 degrees.
To find the size of the smallest angle in a triangle, we need to compare the given angles and determine which one is the smallest.
Let's break down the information given:
The three angles of the triangle are:
1) 3x
2) x + 10
3) 2x - 40
To find the smallest angle, we need to compare these three expressions and check which one has the smallest value.
First, let's simplify the expressions:
1) 3x
2) x + 10
3) 2x - 40
To make a fair comparison, let's rearrange these expressions in ascending order:
1) 2x - 40
2) x + 10
3) 3x
Now, we can see that the smallest angle is given by the expression with the smallest coefficient of x. So, in this case, the smallest angle is 2x - 40.
So, the size of the smallest angle in the triangle is 2x - 40.