Answer:
1.65°
2.m<1=60°
m<2=75°
m<3=55°
m<4=80°
m<5=90°
Step-by-step explanation:
As always,remember that the sum of exterior angles in ANY polygon is 360°.
1.
Given the angles,we must add all of the known angles.
60°+80°+90°=230°
Now,we subtract it to 360°.
360°-230°=130°
But,we are not done yet.It said that the two remaining exterior angles are equal.That mean we need to divide 130 into two equal parts.
130/2=65°
Therefore,the measure of the remaining exterior angles are 65°.
2.
The sum of the measures of the angles must equal to 360°
But first,we need to solve for x.
m<1+m<2+m<3+m<4+m<5=360°
Substituting the expressions:
5x+(6x+3)+(4x+7)+(7x-4)+(9x-18)=360°
Adding Like terms,we get
31x-12=360°
31x=372
x=12
Now all we need to do is substitute x to every measures.
m<1=5x=5(12)=60°
m<2=6x+3=6(12)+3=75°
m<3=4x+7=4(12)+7=55°
m<4=7x-4=7(12)-4=80°
m<5=9x-18=9(12)-18=90°
Therefore the measures of the exterior angles are as follows:
m<1=60°
Checking:
60+75+55+80+90=360
360=360
This proves that our answer is correct.
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Answers & Comments
Answer:
1.65°
2.m<1=60°
m<2=75°
m<3=55°
m<4=80°
m<5=90°
Step-by-step explanation:
As always,remember that the sum of exterior angles in ANY polygon is 360°.
1.
Given the angles,we must add all of the known angles.
60°+80°+90°=230°
Now,we subtract it to 360°.
360°-230°=130°
But,we are not done yet.It said that the two remaining exterior angles are equal.That mean we need to divide 130 into two equal parts.
130/2=65°
Therefore,the measure of the remaining exterior angles are 65°.
2.
The sum of the measures of the angles must equal to 360°
But first,we need to solve for x.
m<1+m<2+m<3+m<4+m<5=360°
Substituting the expressions:
5x+(6x+3)+(4x+7)+(7x-4)+(9x-18)=360°
Adding Like terms,we get
31x-12=360°
31x=372
x=12
Now all we need to do is substitute x to every measures.
m<1=5x=5(12)=60°
m<2=6x+3=6(12)+3=75°
m<3=4x+7=4(12)+7=55°
m<4=7x-4=7(12)-4=80°
m<5=9x-18=9(12)-18=90°
Therefore the measures of the exterior angles are as follows:
m<1=60°
m<2=75°
m<3=55°
m<4=80°
m<5=90°
Checking:
60+75+55+80+90=360
360=360
This proves that our answer is correct.