The measures of the angles of a triangle are shown in the figure below. Find the measure of the smallest angle. (6x+3)° (2x+7)°
The sum of the angles of a triangle is always 180 degrees. So, we can set up an equation to find the value of x:
(6x+3) + (2x+7) + smallest angle = 180
8x + 10 + smallest angle = 180
smallest angle = 180 - 8x - 10
smallest angle = 170 - 8x
To find the smallest angle, we need to find the value of x first. We can do this by setting the two given angles equal to each other:
6x + 3 = 2x + 7
4x = 4
x = 1
Now that we have the value of x, we can find the smallest angle:
smallest angle = 170 - 8(1)
smallest angle = 170 - 8
smallest angle = 162 degrees
Therefore, the measure of the smallest angle in the triangle is 162 degrees.