A right triangle has acute angles measuring 2X plus 6° and 3X −26°. Use the triangle angle some theorem to find the measures of the missing angles of the triangle
To find the measures of the missing angles of the triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
In this case, let's call the acute angles of the right triangle A and B. We are given that:
A = 2X + 6°
B = 3X - 26°
Since we know that the sum of the angles in a triangle is 180 degrees, we can set up the equation:
A + B + 90° = 180°
Substituting the given values:
(2X + 6°) + (3X - 26°) + 90° = 180°
Combine like terms:
5X - 20° + 90° = 180°
Combine further:
5X + 70° = 180°
Subtract 70° from both sides to isolate the variable:
5X = 110°
Divide both sides by 5 to solve for X:
X = 22°
Now that we have the value of X, we can substitute it back into the expressions for A and B to find their specific angle measurements:
A = 2X + 6° = 2(22°) + 6° = 44° + 6° = 50°
B = 3X - 26° = 3(22°) - 26° = 66° - 26° = 40°
Therefore, the missing angles of the triangle are:
A = 50°
B = 40°