The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 62° - 35° = 83°

You need to find the value of a so solve the first equation in terms of z:

a + z = -3
z = -3 - a

then substitute the result (-3 - 1a) into the second equation:

-3a - 6(-3 - a) = -7
-3a + (-6 x -3) + (-6 x -a) = -7
-3a + 18 + 6a = -7
-3a + 6a = -7 - 18
3a = -25
a = \( \frac{-25}{3} \)
a = -8\(\frac{1}{3}\)

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 2) and (2, 6) so the slope becomes:

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)