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.

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

Step-by-step 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.

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