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

Answer 1

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°