Question : In a triangle ABC, the three angles are $x, y$, and $y+10$. Also, $2x-4y=20^{\circ}$. Which type of triangle is ABC?
Option 1: Equilateral
Option 2: Obtuse
Option 3: Acute
Option 4: Right-angled
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Correct Answer: Right-angled
Solution : In a triangle ABC, the three angles are $x,y$, and $y+10$. Also, $2x-4y=20^{\circ}$ The sum of all angles of a triangle is $180^\circ$ $\therefore$ $x+y+y+10=180^{\circ}$ ⇒ $x+2y = 170^{\circ}$.............(1) Given that, $2x-4y=20^{\circ}$.........(2) Solving the above two equations by performing 2(equation 1) + (equation 2), we get: $4x=360^\circ$ ⇒ $x=90^{\circ}$ ⇒ The triangle ABC is right-angled. Hence, the correct answer is Right-angled.
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