Question
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.(4 points) make it 3 sentences sound 7th grade and solve it
Answers
GPT-4o mini
In a right triangle, the sum of the three angles is always 180 degrees. Since one angle is a right angle (90 degrees), we can find the sum of the other two angles, which is 90 degrees. We can write the equation: \( (2x + 6) + (3x - 26) = 90 \).
Now, let's combine like terms:
\( 2x + 3x + 6 - 26 = 90 \)
This simplifies to \( 5x - 20 = 90 \).
Next, add 20 to both sides:
\( 5x = 110 \).
Now, divide by 5:
\( x = 22 \).
Now we can find the measures of the angles:
1. For the first angle: \( 2(22) + 6 = 44 + 6 = 50 \) degrees.
2. For the second angle: \( 3(22) - 26 = 66 - 26 = 40 \) degrees.
So, the angles of the triangle are 90 degrees, 50 degrees, and 40 degrees.
Now, let's combine like terms:
\( 2x + 3x + 6 - 26 = 90 \)
This simplifies to \( 5x - 20 = 90 \).
Next, add 20 to both sides:
\( 5x = 110 \).
Now, divide by 5:
\( x = 22 \).
Now we can find the measures of the angles:
1. For the first angle: \( 2(22) + 6 = 44 + 6 = 50 \) degrees.
2. For the second angle: \( 3(22) - 26 = 66 - 26 = 40 \) degrees.
So, the angles of the triangle are 90 degrees, 50 degrees, and 40 degrees.