The measures of the three angles of a triangle are given. Find the value of x and state whether the triangle is acute, obtuse, or right.
x + 10, x − 20, x + 25
I got x is 55 and it is an acute angle. Is that correct?
checking:
x + 10 + x − 20 + x + 25 = 180
3x = 165
x = 55 , you had that
so the 3 angles are:
65°, 35° , and 80°
You said "it is an acute angle", you must have meant " it is an acute-angled triangle"
80 40
To find the value of x, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
So, we can set up the equation:
(x + 10) + (x - 20) + (x + 25) = 180
Now, let's solve for x:
3x + 15 = 180
3x = 165
x = 55
So, you are correct that x is indeed 55.
To determine whether the triangle is acute, obtuse, or right, we need to analyze the angles.
Substituting x = 55 into the given angle measures, we have:
55 + 10 = 65 degrees
55 - 20 = 35 degrees
55 + 25 = 80 degrees
The triangle is acute when all angles are less than 90 degrees, obtuse when one angle is greater than 90 degrees, and right when one angle is equal to 90 degrees.
In this case, all three angles of the triangle are less than 90 degrees (65, 35, and 80), so the triangle is acute.
Therefore, you are correct that the triangle is acute and x = 55.
To find the value of x and determine the nature of the triangle, we need to use the fact that the sum of all angles in a triangle is always 180 degrees. Let's set up the equation:
(x + 10) + (x - 20) + (x + 25) = 180
Simplifying the equation:
3x + 15 = 180
Subtracting 15 from both sides:
3x = 165
Dividing both sides by 3:
x = 55
So, you are correct that x is 55.
Now, to determine the nature of the triangle, we need to examine the angles. Since x is 55, the three angles are:
55 + 10 = 65 degrees
55 - 20 = 35 degrees
55 + 25 = 80 degrees
To classify the triangle, we compare the angles to the definitions of an acute triangle, obtuse triangle, and right triangle:
- Acute Triangle: All three angles are less than 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees.
- Right Triangle: One angle is exactly 90 degrees.
In this case, none of the angles are greater than 90 degrees, so the triangle is an acute triangle, not a right or obtuse triangle. Therefore, you are correct that the triangle is an acute triangle.