The measure of the smallest angle of a triangle is one-fourth the measure of the largest angle. The measure of the second angle is 36 less than the measure of the largest angle.
Let the smallest angle be x. Then, since the three angles add up to 180,
x + (4x) + (4x-36) = 180
Now find x, and you can figure the angles.
a, b , c
a+b+c=180
a = c/4
b = c-36
so
c/4 + c-36 + c = 180
2.25 c = 216
c = 96
b = c-36 = 60
a = 24
Let the measure of the largest angle be denoted by x.
According to the given information:
- The measure of the smallest angle is one-fourth the measure of the largest angle.
So, the measure of the smallest angle = (1/4)x.
- The measure of the second angle is 36 less than the measure of the largest angle.
So, the measure of the second angle = x - 36.
In a triangle, the sum of all angles is always 180 degrees.
Putting it all together, we can form the equation:
x + (1/4)x + (x - 36) = 180.
Simplifying the equation:
(5/4)x - 36 = 180.
Adding 36 to both sides:
(5/4)x = 216.
Multiplying both sides by 4/5:
x = (216 * 4) / 5.
Simplifying:
x = 864 / 5.
Calculating x:
x ≈ 172.8 degrees.
So, the measure of the largest angle is approximately 172.8 degrees.
The measure of the smallest angle:
(1/4)x = (1/4)(172.8) ≈ 43.2 degrees.
The measure of the second angle:
x - 36 = 172.8 - 36 = 136.8 degrees.
Therefore, the measure of the angles in the triangle are approximately:
Largest angle ≈ 172.8 degrees.
Smallest angle ≈ 43.2 degrees.
Second angle ≈ 136.8 degrees.
To find the measures of the angles in the triangle, let's assume that the largest angle has a measure of x degrees.
According to the given information:
- The smallest angle is one-fourth the measure of the largest angle, so it would be (1/4)x degrees.
- The second angle is 36 less than the measure of the largest angle, so it would be x - 36 degrees.
The sum of all angles in any triangle is always 180 degrees. So, we can write the equation:
Smallest Angle + Second Angle + Largest Angle = 180
(1/4)x + (x - 36) + x = 180
To solve this equation, we need to combine like terms:
(1/4)x + x - 36 + x = 180
Multiplying every term by 4 to get rid of the fraction:
x + 4x - 144 + 4x = 720
Now, we can simplify the arithmetic:
9x - 144 = 720
Next, we can isolate the variable by adding 144 to both sides of the equation:
9x - 144 + 144 = 720 + 144
9x = 864
Finally, divide both sides of the equation by 9 to solve for x:
9x/9 = 864/9
x = 96
Now that we have found the value of x (the largest angle), we can substitute it back into the expressions for the other two angles to find their measures:
- The smallest angle would be (1/4) * 96 = 24 degrees.
- The second angle would be 96 - 36 = 60 degrees.
So, the measures of the three angles in the triangle are:
Largest angle: 96 degrees
Second angle: 60 degrees
Smallest angle: 24 degrees