QuestionAugust 25, 2025

10) The second angle of a triangle is the same size as the first angle. The third angle is 12^circ larger than the first angle. What is the angle measurement of the third angle?

10) The second angle of a triangle is the same size as the first angle. The third angle is 12^circ larger than the first angle. What is the angle measurement of the third angle?
10) The second angle of a triangle is the same size as the first angle. The third angle is 12^circ larger than the first angle. What is the angle measurement of the third angle?

Solution
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Answer

68^{\circ} Explanation 1. Define the angles Let the first angle be x. The second angle is also x, and the third angle is x + 12^{\circ}. 2. Use the triangle angle sum property The sum of angles in a triangle is 180^{\circ}. Therefore, x + x + (x + 12^{\circ}) = 180^{\circ}. 3. Solve for x Simplify the equation: 3x + 12^{\circ} = 180^{\circ}. Subtract 12^{\circ} from both sides: 3x = 168^{\circ}. Divide by 3: x = 56^{\circ}. 4. Calculate the third angle The third angle is x + 12^{\circ} = 56^{\circ} + 12^{\circ}.

Explanation

1. Define the angles<br /> Let the first angle be $x$. The second angle is also $x$, and the third angle is $x + 12^{\circ}$.<br /><br />2. Use the triangle angle sum property<br /> The sum of angles in a triangle is $180^{\circ}$. Therefore, $x + x + (x + 12^{\circ}) = 180^{\circ}$.<br /><br />3. Solve for $x$<br /> Simplify the equation: $3x + 12^{\circ} = 180^{\circ}$. Subtract $12^{\circ}$ from both sides: $3x = 168^{\circ}$. Divide by 3: $x = 56^{\circ}$.<br /><br />4. Calculate the third angle<br /> The third angle is $x + 12^{\circ} = 56^{\circ} + 12^{\circ}$.
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