Question

conrad drew 2 angles. three times the measure of angle 1 is 30 more than 5 time the measure of angle 2. the sum of twice the measure of angle 1 and twice the measure of angle 2 is 180. find the measure of each angle.

Answer 1

Angle 1 = 60° and angle 2 = 30°.

Explanation:

Let the angle 2 be x and the angle 1 by y.

It is given that three times the measure of angle 1 is 30 more than 5 times the measure of angle 2.

Three times the measure of angle 1 = 3y

30 more than 5 times the measure of angle 2 = 30 + 5x

Therefore,

3y = 30 + 5x or

5x - 3y + 30 = 0 --- (1)

It is also given that the sum of twice the measure of angle 1 and twice the measure of angle 2 is 180.

Therefore,

2x + 2y = 180

Divide both sides by 2.

x + y = 90 or

x = 90 - y

Substitute in (1), we get,

5(90 - y) - 3y + 30 = 0

450 - 5y - 3y + 30 = 0

480 - 8y = 0

8y = 480

Divide both sides by 8.

y = 60

x = 90 - y

= 90 - 60

= 30

Hence, angle 1 = 60° and angle 2 = 30°.

Answer 2

Measure of angle 1 is 60° and angle 2 is 30°.

Explanation:

Let us assume Conrad drew two angles ∠1 = x and ∠2 = y.

Now we go through the question.

Three times the measure of angle 1 is 30 more than 5 times the measure of angle 2.

Now we form the equation 3x = 30+5y

⇒ 3x-5y = 30---------(1)

Again the question says,the sum of twice the measure of angle 1 and twice the measure of angle two is 180.

We form the equation again.

⇒ 2x+2y = 180

2(x+y) = 180

Now we divide the equation by 2 on both the sides

⇒ x+y = 90-------(2)

we multiply equation (2) by 5.

⇒ 5(x+y) = 5×90 = 450

⇒ 5x+5y =450---------(3)

Now we add equation (1) and equation (3)

(3x-5y)+(5x+5y)=30+450

3x-5y+5x+5y =480

8x =480

x = 480÷8 = 60

Now we put the value of x in equation (2)

⇒ 60+y =90

⇒ y = 90-60 = 30

So the angle 1 is 60 and angle 2 is 30.