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If one of the interior opposite angles of an exterior angle is 45∘ and the exterior angle is 130∘, what is the measure of the second interior opposite angle?
- a)75∘
- b)85∘
- c)90∘
- d)95∘
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If one of the interior opposite angles of an exterior angle is 45and t...
Using the exterior angle property:
Exterior Angle = Sum of Interior Opposite Angles
130∘= 45∘+ Other Angle
Other Angle = 130∘− 45∘= 85∘
Exterior Angle = Sum of Interior Opposite Angles
130∘= 45∘+ Other Angle
Other Angle = 130∘− 45∘= 85∘
Most Upvoted Answer
If one of the interior opposite angles of an exterior angle is 45and t...
Understanding Exterior and Interior Angles
In geometry, the relationship between an exterior angle and its interior opposite angles is fundamental. The exterior angle is equal to the sum of the two interior opposite angles.
Given Information:
- One interior opposite angle (A) = 45 degrees
- Exterior angle (E) = 130 degrees
Finding the Second Interior Opposite Angle:
To find the second interior opposite angle (B), we can use the formula:
E = A + B
Substituting the known values:
130 = 45 + B
Now, isolate B:
B = 130 - 45
Calculating B:
- B = 130 - 45
- B = 85 degrees
Conclusion:
The measure of the second interior opposite angle is 85 degrees, which corresponds to option 'B'.
This relationship highlights how angles work together in geometry, reinforcing the concept of angle sums.
In geometry, the relationship between an exterior angle and its interior opposite angles is fundamental. The exterior angle is equal to the sum of the two interior opposite angles.
Given Information:
- One interior opposite angle (A) = 45 degrees
- Exterior angle (E) = 130 degrees
Finding the Second Interior Opposite Angle:
To find the second interior opposite angle (B), we can use the formula:
E = A + B
Substituting the known values:
130 = 45 + B
Now, isolate B:
B = 130 - 45
Calculating B:
- B = 130 - 45
- B = 85 degrees
Conclusion:
The measure of the second interior opposite angle is 85 degrees, which corresponds to option 'B'.
This relationship highlights how angles work together in geometry, reinforcing the concept of angle sums.
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Community Answer
If one of the interior opposite angles of an exterior angle is 45and t...
The interior angle is 85°
How?
interior opposite angle =45°
exterior angle =130°
so,130°=45°+ x
X=130° -45°
X=85°
How?
interior opposite angle =45°
exterior angle =130°
so,130°=45°+ x
X=130° -45°
X=85°
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