A right triangle has acute angles measuring 2X plus 6° and 3X −26°. Use the triangle angle some theorem to find the measure of the missing angles of the triangle
Since the triangle is a right triangle, one of the angles must be 90 degrees. Let's call the missing angle Y.
According to the Triangle Angle Sum Theorem, the sum of all angles in a triangle is always 180 degrees.
Therefore, we can set up the following equation:
(2X + 6°) + (3X - 26°) + Y = 180°
Simplifying the equation, we get:
5X - 20° + Y = 180°
Now, let's solve for X and Y:
To do so, we can set up another equation using the fact that the angles of a triangle add up to 180 degrees:
(2X + 6°) + (3X - 26°) + 90° = 180°
Simplifying this equation, we get:
5X - 20° + 90° = 180°
5X + 70° = 180°
Subtracting 70° from both sides, we get:
5X = 110°
Dividing both sides by 5, we get:
X = 22°
Substituting this value back into one of the original equations, we can solve for Y:
5(22°) - 20° + Y = 180°
110° - 20° + Y = 180°
90° + Y = 180°
Subtracting 90° from both sides, we get:
Y = 90°
Therefore, the missing angle Y is 90 degrees. The measure of the missing angles of the right triangle are 90°, 22° + 6° = 28°, and 3(22°) - 26° = 40°.