Question : An exterior angle of a triangle is 115° and one of the interior opposite angles is 45°. The other two angles are:
Option 1: 65° and 70°
Option 2: 60° and 75°
Option 3: 45° and 90°
Option 4: 50° and 85°
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Correct Answer: 65° and 70°
Solution :
Given:
$\angle$ACD = 115°, $\angle$BAC = 45°
We know, $\angle$ABC + $\angle$CAB = $\angle$ACD
⇒ $\angle$ABC = 115° - 45°
$\therefore$ $\angle$ABC = 70°
$\angle$ACB + $\angle$BAC + $\angle$ABC = 180°
⇒ $\angle$ACB + 45° + 70° = 180°
$\therefore$ $\angle$ACB = 180° – 70° – 45° = 65°
Hence, the correct answer is '65° and 70°'.
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