The first angle of a triangle is 24 more than the second. The third angle is twice the first. Find the measure of the angle of the triangle.
Second angle = x
First angle = x +24
Third angle = 2(x+24)
They should add up to 180º.
Solve for x and other angles.
To solve this problem, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's assume that the second angle of the triangle is represented by "x" degrees.
According to the problem, the first angle is 24 degrees more than the second angle. So, the measure of the first angle would be x + 24 degrees.
The problem also states that the third angle is twice the first angle. So, the measure of the third angle would be 2 * (x + 24) degrees.
Now, we can set up an equation using the sum of the angles in a triangle:
x + (x + 24) + 2 * (x + 24) = 180
Simplifying the equation:
x + x + 24 + 2x + 48 = 180
Combining like terms:
4x + 72 = 180
Subtracting 72 from both sides:
4x = 108
Dividing both sides by 4:
x = 27
So, the second angle measures 27 degrees.
Plugging this value back into the expressions for the other angles:
First angle = x + 24 = 27 + 24 = 51 degrees
Third angle = 2 * (x + 24) = 2 * (27 + 24) = 2 * 51 = 102 degrees
Therefore, the measure of the angles of the triangle are 27 degrees, 51 degrees, and 102 degrees.