If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
A. 90°
B. 180°
C. 270°
D. 360°
Answers
the sum of the three exterior angles = 360°
Step-by-step explanation:
If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
Exterior angle of a triangle = (sum of two opposite interior angle)
Sum of all three exterior angle = (∠A + ∠B) + (∠B + ∠C) + (∠C + ∠A)
= 2 ( ∠A + ∠B + ∠C)
= 2 * 180°
= 360°
Another method
three exterior angle would be
180°- ∠A , 180° - ∠B , 180° - ∠C
Sum of all three exterior angle = (180°- ∠A) + (180° - ∠B) + (180° - ∠C)
= 540° - ( ∠A + ∠B + ∠C)
= 540° - 180°
= 360°
the sum of the three exterior angles = 360°
option D is correct
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Answer:
Step-by-step explanation: If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
Exterior angle of a triangle = (sum of two opposite interior angle)
Sum of all three exterior angle = (∠A + ∠B) + (∠B + ∠C) + (∠C + ∠A)
= 2 ( ∠A + ∠B + ∠C)
= 2 * 180°
= 360°
Another method
three exterior angle would be
180°- ∠A , 180° - ∠B , 180° - ∠C
Sum of all three exterior angle = (180°- ∠A) + (180° - ∠B) + (180° - ∠C)
= 540° - ( ∠A + ∠B + ∠C)
= 540° - 180°
= 360°
the sum of the three exterior angles = 360°
option D is correct