How do I find angles c, g and k

a. m<C = 50 deg

b. m<G = 125 deg

c. m<K = 75 deg

Step-by-step explanation:

a.

Look at the two lines marked parallel with 2 marks each.

Angle C and angle 50 deg are alternate interior angles of 2 parallel lines cut by a transversal That makes angle C congruent to the 50-deg angle.

m<C = 50 deg

b.

Angle G is vertical to thh 125-deg angle. Vertical angles are congruent, so m<G = 125 deg

m<G = 125 deg

c.

Look at the two lines marked parallel with one mark each.

Angles e and c are corresponding angles, so they are congruent.

m<E = m<C = 50 deg

The 125 deg angle and angle F are a linear pair, so their measures add up to 180.

f + 125 = 180

m<F = 55 deg

Angles E, F and K are the interior angles of a triangle, so their measures add up to 180 deg.

e + f + k = 180

50 + 55 + k = 180

k = 75

m<K = 75 deg

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