Prove theorems about triangles

a) It is possible and it is the only proper value of angle 2

b) Explanation Below

Angle 1 adds to the two other internal angles to get 180

(angle1) + 30 + 42 = 180

angle1 + 72 = 180

angle1 = 180-72

angle1 = 108 degrees

Subtract this from 180 to find the measure of angle 2

angle2 = 180 - angle1

angle2 = 180-108

angle2 = 72

A shortcut is to use the remote interior angle theorem to add up the interior angles 30 and 42 to get 72 as our exterior angle that is not adjacent to any of the interior angles we just added. Hence the "remote" portion.

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

he earned 78.75 in interest.

step-by-step explanation: