One angle of a triangle is 45* greater than the smallest angle, and the third angle is 5* less than twice the smallest angle. Find the measures of the three angles.
smallest angle --- x
the other is ------ x+45
third ------ 2x - 5
solve for x:
x + x+45 + 2x-5 = 180
x+x+45+2x-5=180
4x+40=180
4x=180-40
4x=140
x =140/4
x=35..
Smallest angle =35
The other is =35+45=80
Third =2X35-5=70-5=65
To solve this problem, let's denote the smallest angle as x.
According to the problem statement, one angle of the triangle is 45 degrees greater than the smallest angle. Therefore, this angle can be expressed as x + 45.
The third angle is given as 5 degrees less than twice the smallest angle. So, it can be expressed as 2x - 5.
To find the measures of the three angles, we need to sum them and set the sum equal to 180 degrees (since the sum of the angles in a triangle is always 180 degrees).
x + (x + 45) + (2x - 5) = 180
Now, let's solve this equation for x:
Combining like terms, we have:
4x + 40 = 180
Subtracting 40 from both sides, we get:
4x = 140
Dividing both sides by 4, we obtain:
x = 35
Now that we have the value of the smallest angle, we can find the measures of the other two angles:
The first angle (x + 45) = 35 + 45 = 80 degrees
The third angle (2x - 5) = (2 * 35) - 5 = 65 degrees
Therefore, the measures of the three angles in the triangle are 35 degrees, 80 degrees, and 65 degrees.