Explanation:
a) If we let x be the measure of the smallest angle, then the measures of the other two angles are 2x + 10 and 2x, respectively. To find x, we need to use the fact that the sum of the angles in any triangle is 180 degrees.
So, we have:
x - 10 + 2x + 2x + 10 = 180
5x = 160
x = 32
Therefore, the measures of the angles are:
Smallest angle: 32
Middle angle: 2 * 32 + 10 = 74
Largest angle: 2 * 32 = 64
b) To determine the type of triangle, we need to compare the measures of its angles.
If all angles are less than 90 degrees, the triangle is an acute triangle.
If one angle is equal to 90 degrees, the triangle is a right triangle.
If one angle is greater than 90 degrees, the triangle is an obtuse triangle.
In this case, since none of the angles are equal to 90 degrees, the triangle is an acute triangle.