Question : Two angles of a triangle are equal and the third angle measures 78°. What is the measure of each of the unknown angles?
Option 1: 50°
Option 2: 51°
Option 3: 49°
Option 4: 52°
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Correct Answer: 51°
Solution : Let the equal angles be $x$. The sum of the three angles of a triangle is 180°. So, $x + x + 78° = 180°$ ⇒ $2x = 180° - 78°$ ⇒ $2x = 102°$ ⇒ $x = 51°$ Hence, the correct answer is 51°.
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Question : The sum of two angles of a triangle is 116° and their difference is 24°. The measure of the smallest angle of the triangle is:
Option 1: 38°
Option 2: 28°
Option 3: 46°
Option 4: 64°
Question : The angles of a triangle are in the ratio 2 : 3 : 7. What is the measure of the largest angle of the triangle?
Option 1: 100°
Option 2: 45°
Option 3: 90°
Option 4: 105°
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°
Question : In $\triangle $ABC, D is a point on side BC such that $\angle$ADC = 2$\angle$BAD. If $\angle$A = 80° and $\angle$C = 38°, then what is the measure of $\angle$ADB?
Option 1: 58°
Option 2: 62°
Option 3: 52°
Option 4: 56°
Question : The vertical angle $\angle A$ of an isosceles $\triangle ABC$ is three times the angle B on it. The measure of the $\angle A$ is:
Option 1: 90°
Option 2: 108°
Option 3: 100°
Option 4: 36°
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