Respuesta :
Answer:
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.
Answer:
Angle 1 = 60° and angle 2 = 30°.
Step-by-step 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°.
