An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 69° - 49° = 62°

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 42 as well and sum (Inside, Outside) to equal 13. For this problem, those two numbers are 6 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 13y + 42
y² + (6 + 7)y + (6 x 7)
(y + 6)(y + 7)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-5x - 6 = \( \frac{x}{5} \)
5 x (-5x - 6) = x
(5 x -5x) + (5 x -6) = x
-25x - 30 = x
-25x - 30 - x = 0
-25x - x = 30
-26x = 30
x = \( \frac{30}{-26} \)
x = -1\(\frac{2}{13}\)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)