The angles in a triangle are such that one angle is 108 degrees more than the smallest angle, while the third angle is 4 times as large as the smallest angle. Find the measures of all three angles
Oh, this is kinda hard. Uh, does it show you a diagram of the triangle?
To solve this problem, let's denote the measure of the smallest angle as "x".
According to the given information:
- One angle is 108 degrees more than the smallest angle: This can be expressed as x + 108.
- The third angle is 4 times as large as the smallest angle: This can be expressed as 4x.
We know that the sum of the angles in a triangle is always equal to 180 degrees. Therefore, we can set up the following equation to solve for x:
x + (x + 108) + 4x = 180
Combining like terms, we have:
6x + 108 = 180
Next, we can isolate x by subtracting 108 from both sides of the equation:
6x = 180 - 108
Simplifying further:
6x = 72
Now, we can solve for x by dividing both sides of the equation by 6:
x = 12
So, the measure of the smallest angle is 12 degrees.
To find the measures of the other two angles, we can substitute the value of x back into the expressions we derived earlier:
One angle = x + 108 = 12 + 108 = 120 degrees
The third angle = 4x = 4 * 12 = 48 degrees
Therefore, the measures of all three angles in the triangle are: 12 degrees, 120 degrees, and 48 degrees.
The angles of a triangle add up to 180°
So, if the smallest is x, we have
x + x+108 + 4x = 180
6x = 72
x = 12
So now figure the other two angles.