Please help answer this

Question

If the measure of angle DTJ is equal to 20(1/7x+2) and it’s supplement on line DM is equal to 4/5 times the measure of angle DTJ, then determine the angle measure of angle DTJ

Answer 1

Measure of DTJ = 20 (1/7 x + 2)

Let measure of Supplement of DTJ = y

DTJ plus its supplement = 180 So.....[20 (1/7 x + 2)] + y = 180

The suppplement of DTJ is 4/5 times m of DTJ So... y = 4/5[20 (1/7 x + 2)]

We now have system of two equations with two variables

.[20 (1/7 x + 2)] + y = 180

y = 4/5[20 (1/7 x + 2)]

Solve from there....

Answer 2

Since supplement angles mean that their values add together to equal 180˚, we can use this information to solve for x, and then solve for the angle measure of angle DTJ.

(angle DTJ) + (supplement of angle DTJ) = 180

Since the question states that the supplement of angle DTJ is equal to 4/5(measure of angle DTJ), we substitute that in:

(angle DTJ) + 4/5(angle DTJ) = 180

Since we know the value of the measure of angle DTJ is 20 (1/7x + 2), we substitute that in.

20 (1/7x + 2) + 4/5 (20 (1/7x + 2)) = 180

I'm not exactly sure if you meant (1/7)x or (1/(7x)), but I assumed you meant the first (however, if you meant the latter, feel free to let me know and I'll solve that problem for you!)

Now, I will distribute the 20 to the ((1/7)x + 2) and the 4/5 to the 20 ((1/7)x + 2):

(20/7)x + 40 + 16 ((1/7)x + 2) = 180

Now, I will distribute the 16 to the ((1/7)x + 2):

(20/7)x + 40 + (16/7)x + 32 = 180

Now, I will add like terms, namely (20/7)x with (16/7)x and 40 with 32:

(20/7)x + (16/7)x + 40 + 32 = 180

(36/7)x + 72 = 180

Now, I will start to isolate the x by subtracting 72 from both sides.

(36/7)x + 72 - 72 = 180 - 72

(36/7)x = 108

Now, I will isolate x by multiplying both sides by 7/36, since it will cancel out the 36/7 on the left side.

(7/36) * (36/7)x = 108 * (7/36)

x = 21

Therefore, since the angle measure of DTJ is given as 20 ((1/7)x + 2), we substitute x = 21 in.

angle DAG = 20 ((1/7)x + 2) = 20 ((1/7)(21) + 2) = 20 (3 + 2) = 20 (5) = 100˚