Two angles are supplementary. The measure of the larger angle is 4 more than 3 times the measure of the smaller angle. Find the measures of both angles

The measures of both angles are 136 degrees and 44 degrees

Step-by-step explanation:

we know that

If two angles are supplementary, then their sum is equal to 180 degrees

Let

x ----> the measure of the larger angle

y ---> the measure of the smaller angle

we have that

----> equation A

----> equation B

Solve the system by substitution

substitute equation B in equation A

solve for y

Find the value of x

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4