Two angles are supplementary. The measure of the smaller angle is four more than one third the measure of the larger angle. The measure of the larger angle is

The measure of smaller and larger angles will be 48 degrees and 132 degrees, respectively.

Given information:

The two angles are supplementary. Let them be x (larger) and y (smaller).

The measure of the smaller angle is four more than one-third the measure of the larger angle.

The above condition can be written as,

Supplementary angles are the angles whose sum of measure is equal to 180 degrees.

So,

Solve the above two equations as,

Therefore, the measure of smaller and larger angles will be 48 degrees and 132 degrees, respectively.

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132

Step-by-step explanation:

2 Angles are supplementary:

x + y = 180

The smaller angle is four more than one third of other:

y = 1/3x + 4

Plug in y into the original equation:

x + 1/3x + 4 = 180

Solve the equation:

4/3x = 176

x = 176 * 3/4

x = 132

y = 48

x is the larger angle so 132 is the answer

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