A side of the triangle below has been extended to form an exterior angle of 159º. Find the value of x.

x = 69

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles in a triangle

x+90 = 159

Subtract 90 from each side

x +90-90 = 159-90

x =69

One of the interior angles is given as 90°

Move on to the exterior angle with 159°. Since one part of the altitude is given to be 159°, we can find the other part (let's name it y) because both add up to 180°(linear pair).

159+y = 180

y = 180-159

y = 21°

Now finally find x.

All the interior angles of the triangle result up to 180°

90+21+x = 180

111+x = 180

x = 180-111

x = 69°

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be