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Question
An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to
Options
75°
80°
80°
40°
50°
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Solution
n the ΔABC, CD is the ray extended from the vertex C of ΔABC. It is given that the exterior angle of the triangle is 100° and two of the interior opposite angles are equal.
So, ∠ACD = 100° and A = ∠B
So, now using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get.
In ΔABC
∠A + ∠B = ∠ACD
∠2A = 100°
`∠A = (100°)/2`
∠A = 50°
∠A = ∠B = 50°
Therefore, each of the two opposite interior angles is 50°.
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