in a triangle,the largest angle is 29 degrees more than the smallest.The third angle is 13 degrees larger than the smallest. What is the smallest angle in the triangle?What kind of triangle is it?
and show work please.
To solve this problem, let's start by assigning variables to the three angles in the triangle.
Let's call the smallest angle x degrees.
According to the problem, the largest angle is 29 degrees more than the smallest. Therefore, the largest angle is x + 29 degrees.
The third angle is 13 degrees larger than the smallest, so it is x + 13 degrees.
To find the smallest angle in the triangle, we need to add up the measures of all three angles and set the sum equal to 180 degrees (the total sum of angles in a triangle).
So, x + (x + 29) + (x + 13) = 180.
Now, let's solve this equation to find the value of x, which represents the smallest angle.
Combining like terms, the equation becomes:
3x + 42 = 180.
Subtracting 42 from both sides of the equation gives us:
3x = 138.
Dividing both sides of the equation by 3, we get:
x = 46.
Therefore, the smallest angle in the triangle is 46 degrees.
To determine the type of triangle, we can compare the angles.
The largest angle is x + 29 = 46 + 29 = 75 degrees.
The third angle is x + 13 = 46 + 13 = 59 degrees.
Considering the measures of the angles, we see that we have a triangle with one obtuse angle (75 degrees) and two acute angles (46 degrees and 59 degrees).
Therefore, the type of triangle in this case is an obtuse-angled triangle.