Question : In a triangle ABC, the three angles are $x, y$ , and $y + 10$ . Also, $2 x - 4 y = 20^{\circ}$ . Which type of triangle is ABC?
Option 1: Equilateral
Option 2: Obtuse
Option 3: Acute
Option 4: Right-angled

Question

Question : x, y, and z are the sides of a triangle. If z is the largest side and x²+ y² > z², then the triangle is a:
Option 1: Isosceles right angled triangle
Option 2: Acute angled triangle
Option 3: Obtuse angled triangle
Option 4: Right angled triangle

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Answer 1

Correct Answer: Right-angled

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

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Question : In a triangle ABC, the three angles are x,y, and y+10. Also, 2x−4y=20∘. Which type of triangle is ABC?Option 1: EquilateralOption 2: ObtuseOption 3: AcuteOption 4: Right-angled

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Question : In a triangle ABC, the three angles are $x, y$ , and $y + 10$ . Also, $2 x - 4 y = 20^{\circ}$ . Which type of triangle is ABC?
Option 1: Equilateral
Option 2: Obtuse
Option 3: Acute
Option 4: Right-angled