A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Let's use this theorem to find the measure of the third angle in the right triangle.
We know that one of the acute angles measures 2x+6 degrees and the other measures 3x−26 degrees.
So,
2x+6 + 3x−26 + 90 = 180
5x - 20 = 90
5x = 110
x = 22
Now we can find the measures of the missing angles:
2x+6 = 2(22)+6 = 50 degrees
3x−26 = 3(22)−26 = 40 degrees
Therefore, the measures of the missing angles of the right triangle are 40 degrees and 50 degrees.
Well, well, well, we've got ourselves a right-angled triangle with some angles missing. Let's dive into it!
According to the Triangle Angle Sum Theorem, the sum of all angles in a triangle is 180 degrees. So, we have:
(2x + 6) + (3x - 26) + 90 = 180
Now, let's solve this equation and find the missing angles:
5x - 20 + 90 = 180
5x + 70 = 180
5x = 110
x = 22
Now we can substitute the value of x into the angles to find their measures.
Angle 1: 2x + 6 = 2(22) + 6 = 50 degrees
Angle 2: 3x - 26 = 3(22) - 26 = 40 degrees
So, the missing angles of the right triangle measure 50 degrees and 40 degrees respectively.
Now that we've solved the mystery of the missing angles, it's a triangle well-rounded with humor and math! Keep those angles nice and acute!
To find the measures of the missing angles in the right triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle equals 180 degrees.
In a right triangle, one of the angles is always 90 degrees. Let's denote this angle as angle A.
Given that angle A measures 90 degrees and the other two angles are 2x+6 degrees and 3x-26 degrees, let's set up the equation:
(angle A) + (angle B) + (angle C) = 180 degrees
Substituting the given values, we have:
90 + (2x+6) + (3x-26) = 180
Combining like terms, we get:
2x + 3x + 90 + 6 - 26 = 180
Simplifying further, we have:
5x + 70 = 180
Now, we can solve for x by isolating the term with x:
5x = 180 - 70
5x = 110
Dividing both sides by 5:
x = 110 / 5
x = 22
Now that we have the value of x, we can substitute it back into the expressions for angle B and angle C to find their measures:
angle B = 2x + 6
= 2(22) + 6
= 44 + 6
= 50 degrees
angle C = 3x - 26
= 3(22) - 26
= 66 - 26
= 40 degrees
So, the measures of the missing angles in the right triangle are:
angle B = 50 degrees
angle C = 40 degrees
The Triangle Angle Sum Theorem states that the sum of all angles in a triangle is 180 degrees.
To find the measures of the missing angles of the right triangle, we can use the fact that one angle is 90 degrees.
Given that the acute angles of the triangle are 2x+6 degrees and 3x-26 degrees, we can set up an equation to find x:
(2x + 6) + (3x - 26) + 90 = 180
Combine like terms:
5x - 20 = 180
Add 20 to both sides of the equation:
5x = 200
Divide both sides by 5:
x = 40
Now that we have found x, we can substitute it back into the expressions for the acute angles to find their measures:
First angle: 2x + 6 = 2(40) + 6 = 86 degrees
Second angle: 3x - 26 = 3(40) - 26 = 94 degrees
So, the measures of the missing angles of the right triangle are 86 degrees and 94 degrees.