The three angles of a triangle have measures 8x+6, 7x-8, 5x+2. What is the measure of the smallest angle?
To find the measure of the smallest angle in a triangle, we need to determine the actual values of the three angles.
We're given the measures of the angles as expressions: 8x+6, 7x-8, and 5x+2.
To find the values of x, we can set up an equation, knowing that the sum of the angles in a triangle is always 180 degrees:
(8x+6) + (7x-8) + (5x+2) = 180
Now we can solve for x:
8x + 6 + 7x - 8 + 5x + 2 = 180
Combine like terms:
20x = 180
Divide both sides by 20:
x = 9
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their actual measures:
Angle 1 = 8x + 6 = 8(9) + 6 = 78
Angle 2 = 7x - 8 = 7(9) - 8 = 55
Angle 3 = 5x + 2 = 5(9) + 2 = 47
Now we can determine the smallest angle by comparing the three measures:
The measure of the smallest angle is 47 degrees.
they add up to 180, so
8x+6 + 7x-8 + 5x+2 = 180
solve for x, then decide which is the smallest angle.
I suspect it is 5x+2