Question
A side of the triangle below has been extended to form an exterior angle of 141°. Find the value of xx.
Answers
Answer
wrong.
Answered by
GPT 3.5
A triangle has interior angles that sum to 180°, so since a 141° exterior angle was formed by extending one side, the corresponding interior angle is 180° - 141° = <<180-141=39>>39°. Thus, the other two interior angles have a sum of 180° - 39° = 141°. Since a triangle only has 3 interior angles, these two angles must each be 141°/2 = <<141/2=70.5>>70.5°. Since angle x is adjacent to one of these 70.5° angles, we see that x = 180° - 70.5° = <<180-70.5=109.5>>109.5°. Thus, the value of x is x = <<109.5=109.5>>109.5°. Answer: \boxed{109.5}.
Answered by
GPT 3.5
Apologies for the mistake. Let's correct it.
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle is 141°, and one of the opposite interior angles is x°. Therefore, the other opposite interior angle is 141° - x°.
Since the sum of the angles in a triangle is 180°, we have the equation:
x° + (141° - x°) + 39° = 180°
Combining like terms, we get:
180° - x° + 39° = 180°
Simplifying further:
219° - x° = 180°
Subtracting 219° from both sides:
-x° = -39°
Dividing both sides by -1:
x° = 39°
Therefore, the value of x is x = 39°.
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle is 141°, and one of the opposite interior angles is x°. Therefore, the other opposite interior angle is 141° - x°.
Since the sum of the angles in a triangle is 180°, we have the equation:
x° + (141° - x°) + 39° = 180°
Combining like terms, we get:
180° - x° + 39° = 180°
Simplifying further:
219° - x° = 180°
Subtracting 219° from both sides:
-x° = -39°
Dividing both sides by -1:
x° = 39°
Therefore, the value of x is x = 39°.