In the diagram below, determine the value of x:

9514 1404 393

  55°

Step-by-step explanation:

130° is an external angle to the small triangle at lower left, so is the sum of the remote interior angles. The unmarked interior angle at the bottom of that triangle is then 130° -30 = 100°.

That is an exterior angle of the large triangle that has remote interior angles of 45° and x°. So, ...

  x° + 45° = 100°

  x° = 100° -45°

  x° = 55°

Alternate solution

The sum of the interior angles of a quadrilateral is 360°. Three of the angles in the bounding quadrilateral are x°, 45°, 30°. The fourth is the reflex angle that is (360° -130°) = 230°. So, we have ...

  x° +45° +230° +30° = 360° . . . . . angles CCW from lower right

  x° = 360° -305°

  x° = 55°

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

b.-4 units

all you   do is count how many times you move