Three angles of a triangle are (x - 15)°, (x + 45)°, and (x + 60)°. Identify the type of triangle.
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Correct answer: B
Explanation
The correct answer is option 2 i.e. Right angle triangle.
Sum of the angles: (x - 15) + (x + 45) + (x + 60) = 180
Simplifying: 3x + 90 = 180
Subtract 90 from both sides: 3x = 90
Divide by 3: x = 30
Now substitute x = 30° in each angle:
First angle: (x - 15) = 30 - 15 = 15°
Second angle: (x + 45) = 30 + 45 = 75°
Third angle: (x + 60) = 30 + 60 = 90°
The angles of the triangle are 15°, 75°, and 90°.
Since one angle is 90°, the triangle is a right-angled triangle.