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The unknown angle is 50 degrees.

The solution to the equation 3^(x+2) = 2^(x+3) is found by taking the natural logarithm of both sides, applying logarithm properties, isolating x, and simplifying to an expression involving natural logarithms of 2 and 3. The approximate value of x is then calculated.

The expression $((i+1)(i-1))^2$ simplifies to 4.

The solution to the problem \sqrt{25\%} + \sqrt{49\%} is 1.2, which is equivalent to 120%.

To find x, the exterior angle theorem is used, along with the knowledge that a right angle is 90 degrees, to solve for x, which equals 45 degrees.

The solution to the equation involving radicals and exponents is x = 77/120.

The water lily takes 47 days to cover half the pond, given that it doubles in size each day and covers the entire pond on day 48.

The equation 3^(x^2)/9^x = 81 is solved by rewriting the equation with the same base, simplifying the denominator, applying the quotient rule for exponents, equating the exponents, rearranging into a quadratic equation, and finally using the quadratic formula to find the two solutions, x = 1 + √5 and x = 1 - √5.

The unknown angle in a triangle, formed by two slanted lines and a vertical line, with two given angles of 80 degrees each, is calculated to be 20 degrees using the triangle angle sum property.

The equation x^2 + 3x + 7 = 6/(x^2 + 3x + 2) is solved by substituting u = x^2 + 3x, resulting in a quadratic equation in u. Factoring the quadratic equation yields two possible values for u, which are then substituted back into the substitution to find the solutions for x using the quadratic formula. One case results in two real solutions, while the other yields no real solutions.