I don't understand, help.

9514 1404 393

Step-by-step explanation:

The hash marks indicate that the lower triangle is isosceles. That means its base angles are equal. The external angle marked 40° will be the sum of those two equal angles, so ...

  x + x = 40°

  x = 20°.

x is one of the two acute angles in the right triangle. The other is y, which is the complement of x.

  y = 90° -x = 90° -20°

  y = 70°

Additional comments

The angle marked 40° is one of a "linear pair". The other angle in that pair is the obtuse angle in the lower triangle. Its measure is 180°-40° = 140°. The two base angles of that isosceles triangle are both x°, so you have ...

  x° +x°+140° = 180°

  2x° = 180° -140° = 40°

That is, the sum of the two angles will be equal to the external angle marked 40°. The relevant theorem says "an exterior angle is equal to the sum of the remote interior angles." Remembering this is a useful shortcut, so you don't have to find the third interior angle, which is 140° in this case.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)