one of the exterior angles of a triangle is 100 degree and its interior opposite angles are equal to each other what measure of each of these two angles are?
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Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior
opposite angles of the triangle.
Let AABC be a triangle where the side
BC is produced.
By the theorem we have
ZA + B = 100°
(1)
It is given that the interior opposite angles are equal i.e., ZA = ZB.
..Equation (1) becomes
2ZA = 100°
+ ZA = 50°
» ZB = 50°
Using angle sum property of a triangle, Sum of all angles of a triangle = 180° =
+ ZA + ZB + ZC = 180°
= 100 + X = 180° [from (1)] > ZC = 180° – -100°
+ ZC = 80°.
Hence ZA = 50°
ZB = 50°
ZC = 80°.
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